Factors, multiples & primes

Eight cards with numbers on them are shown below.

Jo has four of these cards in her hand.

Dafydd chooses one of Jo’s four cards at random.

• There is an even chance that the number on the card is a square number.

• It is unlikely that the number on the card is a factor of 21.

Which four cards could Jo have in her hand?

Write the numbers on the four cards below.

What is four times three hundred and seventy-two?

Write your answer in figures.

Write 1·52 in words.

Insert one pair of brackets into the calculation below to make it correct. 4 x 7 + 3 – 1 = 39

Write the following numbers in ascending order.

3·2, – 4, 3·09, –1

Write down the first three multiples of 67.

A number has exactly six factors. Its factors are 1, 2, 5, 10, 25 and the number itself.

What is the number?

Using only the numbers listed below,

120 121 122 123 124 125 126

write down

a square number,

a cube number,

a multiple of 14.

Using only the numbers listed below,

120 121 122 123 124 125 126

write down

a square number,

a cube number,

a multiple of 14.

Write down, in figures, the number four hundred thousand, one hundred and eight.

Stef uses each of the digits 4, 5, 9 and 3 to make a four-digit number.

What is the largest number that she can make that is a multiple of 5?

Write down all the factors of 20.

Express 945 as a product of its prime factors in index form.

There is one square number between 180 and 200.

What is this square number?

A number has exactly four factors. All of the factors are less than 30. Three of the factors are 1, 2 and 26.

What is the other factor?

In this part of the question, you will be assessed on the quality of your accuracy in writing.

Which length is exactly halfway between 280 m and 410 m? You must show all your working. [2 + 1 W]

In this question, you will be assessed on the quality of your organisation and communication.

Dyfrig has 50 cards. His cards are numbered from 1 to 50.

Dyfrig puts a red sticker on every card that has a multiple of 6 on it. He puts a blue sticker on every card that has a multiple of 8 on it.

Some cards will have both a blue sticker and a red sticker on them. What numbers will be on these cards? You must show all your working. [3 + 1 OC]

Calculate the value of n.

You must show all your working.

Calculate the value of n.

You must show all your working.

Arwyn doubles the number fifty-three thousand.

Write Arwyn’s answer in figures.

Write 3572 correct to the nearest 100.

A decimal number is written on a card.

You have three clues to help you work out the number on the card. Clue 1: The number is between 5 and 12 inclusive. Clue 2: The number is a multiple of 2·3. Clue 3: The square of the number is greater than 50 but less than 120.

What is the decimal number on the card?

Express 495 as a product of its prime factors in index form.

Explain how your answer to part (a) tells you that 495 is not a square number.

Find the Highest Common Factor (HCF) of 495 and 60.

A pencil case contains some pens. One pen is chosen at random. The probability that the chosen pen is blue is 45%.

What is the probability that the chosen pen is not blue?

Dewi throws a fair six-sided dice. What is the probability that Dewi throws a prime number?

Circle your answer.

A decimal number is written on a card.

You have three clues to help you work out the number on the card. Clue 1: The number is between 5 and 12 inclusive. Clue 2: The number is a multiple of 2·3. Clue 3: The square of the number is greater than 50 but less than 120.

What is the decimal number on the card?

Express 495 as a product of its prime factors in index form.

Explain how your answer to part (a) tells you that 495 is not a square number.

Find the Highest Common Factor (HCF) of 495 and 60.

Express 675 as a product of its prime factors in index form.

360 expressed as a product of its prime factors in index form is 2³ × 3² × 5.

What is the smallest whole number that 360 can be multiplied by to give a square

number?

Smallest whole number is_........

Which one of the following fractions can be written as a recurring decimal?

Circle your answer.

Which three numbers from the list below are prime numbers?

27 31 35 39 43 47 51 55

The three prime numbers are:

Give your answer correct to 2 significant figures.

Calculate the reciprocal of 23.

Give your answer correct to 3 decimal places.

Circle the correct answer for each of the following.

The Lowest Common Multiple (LCM) of 4 and 6 is:

2 4 6 12 24

The Highest Common Factor (HCF) of 10 and 15 is:

5 10 15 30 150

Express 675 as a product of its prime factors in index form.

360 expressed as a product of its prime factors in index form is 2³ × 3² × 5.

What is the smallest whole number that 360 can be multiplied by to give a square

number?

Smallest whole number is_........

Give your answer correct to 2 significant figures.

Calculate the reciprocal of 23.

Give your answer correct to 3 decimal places.

Circle the correct answer for each of the following.

The Lowest Common Multiple (LCM) of 4 and 6 is:

2 4 6 12 24

The Highest Common Factor (HCF) of 10 and 15 is:

5 10 15 30 150

Using only the numbers in the following list,

31 33 35 37 39 41 43

find

the multiple of 5·5,

The multiple of 5·5 is_........

the factor of 111.

The factor of 111 is_........

Two friends, Geraint and Dyfrig, are having a discussion.

Explain why Geraint is incorrect.

Dyfrig says,

“All cube numbers are odd numbers.”

Explain why Dyfrig is incorrect.

One of the calculations below is incorrect.

Circle the incorrect calculation.

One of the numbers below is a multiple of 38.

Circle the multiple of 38.

2 19 338 388 3838

Computers cost £432 each.

How many can be bought with £9876?

Find the whole number that satisfies all of the following conditions:

• It is a whole number between 15 and 35 inclusive. • The number is a multiple of 2 but not a multiple of 4.

• 3 is a factor of this number, but 9 is not a factor of this number.

The whole number is_{……………………………………}

Explain why Geraint is incorrect.

Dyfrig says,

“All cube numbers are odd numbers.”

Explain why Dyfrig is incorrect.

Using only the numbers in the following list,

31 33 35 37 39 41 43

find

the multiple of 5·5,

The multiple of 5·5 is_........

the factor of 111.

The factor of 111 is_........

Express 1575 as a product of its prime factors in index form.

Find the whole number that satisfies all of the following conditions:

• It is a whole number between 15 and 35 inclusive. • The number is a multiple of 2 but not a multiple of 4.

• 3 is a factor of this number, but 9 is not a factor of this number.

The whole number is_{……………………………………}

Express 1575 as a product of its prime factors in index form.

Find a whole number value of n, so that 7n 9 is a multiple of 4.

You must show all your working.

When n =_........ , 7n 9 is a multiple of 4.

Find a whole number value of n, so that 3n 5 is a prime number.

You must show all your working.

When n =_........ , 3n 5 is a prime number.

Write down the first 4 multiples of 48.

Circle the prime number below.

3 4 6 8 9

A number has exactly four factors. Its factors are 1, 3, 13 and the number itself.

What is the number?

Elaine writes down two square numbers.

She subtracts the smaller square number from the larger square number. Her answer is 9.

Which two square numbers did Elaine write down?

Elaine’s square numbers are_........ and_........

In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.

Geraint writes down three different even numbers.

The range of his numbers is 4.

Which three different even numbers did Geraint write down?

You must show all your working.

Two fair spinners are shown in the diagram above. In a game, the two spinners are spun.

The two numbers obtained are multiplied together to get a score. For example, in the diagram above, the score is 6 because 3 2 6.

Some of the scores are shown in the table below.

Complete the table to show all the possible scores.

Explain why all the scores are even numbers.

What is the probability that a person gets a score of 10 or more when playing the game

once?

Players are charged £2.50 to play the game once. Each player who gets a score of 10 or more wins £3.50. How much profit would you expect to make when 228 people each play the game once?

You must show all your working.

Find a whole number value of n, so that 7n 9 is a multiple of 4.

You must show all your working.

When n =_........ , 7n 9 is a multiple of 4.

Find a whole number value of n, so that 3n 5 is a prime number.

You must show all your working.

When n =_........ , 3n 5 is a prime number.

Two fair spinners are shown in the diagram above. In a game, the two spinners are spun.

The two numbers obtained are multiplied together to get a score. For example, in the diagram above, the score is 6 because 3 2 6.

Some of the scores are shown in the table below.

Complete the table to show all the possible scores.

Explain why all the scores are even numbers.

What is the probability that a person gets a score of 10 or more when playing the game

once?

Write 95 048 in words.

Find the sum of 872 and 59.

Multiply 250 by 5.

Write down all the factors of 18.

The factors of 18 are_........

Which one of these numbers is both a square number and an even number?

Circle the correct answer.

2 9 12 16 17

Write 75% as a fraction in its lowest terms.

Write down the mode of these numbers.

28 31 28 29 31 28 34 24 32

Find the Lowest Common Multiple (LCM) of 60 and 72.

LCM of 60 and 72 is_{…………........ ……….}

Express 882 as a product of its prime factors.

Give your answer in index form.

One of these fractions can be written as a recurring decimal.

Circle this fraction.

Which one of the following numbers is a factor of 92?

Circle your answer.

31 23 29 36 6

Which one of the following numbers is a multiple of 17?

Circle your answer.

1953 1653 2053 1853 1753

Find the Lowest Common Multiple (LCM) of 60 and 72.

LCM of 60 and 72 is_{…………........ ……….}

Express 882 as a product of its prime factors.

Give your answer in index form.

Write the number three million, seven hundred thousand in figures.

In the boxes below, write the largest possible four-digit even number.

You may use digits more than once.

Write down all the factors of 15.

The factors of 15 are_........

Kate writes down three different even numbers.

The mean of Kate’s numbers is 8. She did not write down the number 8.

What possible even numbers could Kate have written down?

Possible numbers Kate could have written are_{……........ ……},_{……........ ……} and_{……........ ……}

Evaluate 5·4³ × 3·7².

Give your answer correct to the nearest 10.

Find 62% of 7·8.

Which one of the following numbers is a multiple of 19?

Circle your answer.

91 151 199 219 247

Which one of the following numbers is a cube number?

Circle your answer.

1197 2197 3197 4197 5197

On each Venn diagram, shade the region that represents the given set.

Evaluate 5·4³ × 3·7².

Give your answer correct to the nearest 10.

Find 62% of 7·8.

Which one of the following numbers is a multiple of 19?

Circle your answer.

91 151 199 219 247

Which one of the following numbers is a cube number?

Circle your answer.

1197 2197 3197 4197 5197

On each Venn diagram, shade the region that represents the given set.

Sara has 20 balls in a bag. There are 15 blue balls and 5 red balls. Sara chooses a ball at random from her bag.

Describe the chance that Sara chooses a red ball from her bag.

Circle the correct expression from those given below.

impossible unlikely an even chance likely certain

Gareth has some cards with a number written on each one. These are Gareth’s cards.

Gareth chooses one of his cards at random.

Describe the chance that Gareth chooses a card with an odd number on it.

Circle the correct expression from those given below.

impossible unlikely an even chance likely certain

Find the whole number which satisfies all of the following conditions:

• It is a whole number between 1 and 40 inclusive.

• The number is a multiple of 4 but not a multiple of 8.

• 3 is a factor of this number.

• The number is a square number.

The whole number is_{……………........ ………..}

Find the whole number which satisfies all of the following conditions:

• It is a whole number between 1 and 40 inclusive.

• The number is a multiple of 4 but not a multiple of 8.

• 3 is a factor of this number.

• The number is a square number.

The whole number is_{……………........ ………..}

Add 3874 and 649.

Subtract 532 from 700.

Write down all the factors of 27.

The factors of 27 are_........

A Venn diagram is used to show the following information:

• The Universal set, ε, is the set of numbers from 10 to 20 inclusive. • Set A = {11, 13, 14, 18, 20}. • Set B = {multiples of 3}.

Draw the Venn diagram that shows the above information.

Solve the following equations.

13f + 2 = 6f + 5.

n is an integer.

Tick the correct statement below.

You must give an explanation for your decision.

Write down the first 3 multiples of 47.

One of the numbers below is a factor of 676.

Circle the correct number.

22 32 42 52 62

When one of the numbers below is divided by 22, there is a remainder of 11.

Circle the correct number.

208 209 210 211 212

Bethan writes down two square numbers.

She adds her two numbers together. Her answer is a square number less than 30.

Which two square numbers did Bethan write down?

Bethan’s square numbers are_{……........ ……} and_{……........ ……}

Harri adds three even numbers together and gets an answer of 23.

Explain how you know that Harri’s answer is incorrect.

Factorise 10 a – 15.

Solve the following equations.

13f + 2 = 6f + 5.

n is an integer.

Tick the correct statement below.

You must give an explanation for your decision.

Express 315 as a product of its prime factors in index form.

What is the Highest Common Factor (HCF) of 315 and 42?

Express 315 as a product of its prime factors in index form.

What is the Highest Common Factor (HCF) of 315 and 42?

Jo thinks of a number. Her number lies between 30 and 50. Jo’s number is a multiple of 3. Jo’s number is also a multiple of 7.

What number does Jo think of?

Place the numbers 1, 2, 3, 4, 5 in the Venn diagram below.

Space for working:

Write thirteen point two five in figures.

Write the number 60 043 in words.

Here are four digits:

8 5 3 7

Use each of these digits once and once only.

What is the largest number that can be made?

Use three of these digits once and once only.

What is the smallest even number that can be made?

One of the numbers below is a multiple of 13.

Circle the correct answer.

2226 3213 1628 2843 6110

Efa thinks of two whole numbers. She multiplies her numbers together. She then adds 12. The answer is 120.

What two numbers could Efa have been thinking about?

Efa’s two numbers could be_{…........ ……} and_{…........ ……}

Jac thinks of a number. 25% of his number is 35.

You must show all your working.

One of the values below is the solution to k + 3 = 6·9

Circle the correct answer.

2·3 20·7 3·9 9·9 207

Simplify the expression 12w + 15w – w.

Write down the next term in the following sequence.

Describe in words the rule for continuing the following sequence.

4, 12, 36, 108, …

Look at the sequence:

8, 16, 24, 32, …

Will any of the first 100 terms of this sequence be a prime number?

Explain how you know.

In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.

Mair draws three different rectangles. Each rectangle has an area of 20 cm². Each of the sides of her rectangles is a whole number of centimetres.

Find the perimeter of each of Mair’s rectangles.

You must show all your working.

Consider the following list of numbers:

4 25 27 36 49 64 90 125

Using only the numbers in the list above, write down

the three cube numbers,

a number that is both a square number and a multiple of 9,

a number that is a factor of 81.

Using only two numbers from the list, fill in the spaces in the following statement:

‘Dividing_........ by_......... and then rounding the answer to the nearest 10, gives an answer of 30.’

Display the following information in a Venn diagram.

• Universal Set (ε): Integers between 74 and 80 inclusive.

• Set A: Even numbers.

• Set B: Multiples of 3.

Jonathan writes a whole number on a card.

• The number is between 55 and 83 inclusive.

• The square root of the number is greater than 8 but less than 9.

• The highest common factor (HCF) of 49 and the number is 7.

What number is on Jonathan’s card?

The number on Jonathan’s card is_{………........ ……………..}

Display the following information in a Venn diagram.

• Universal Set (ε): Integers between 74 and 80 inclusive.

• Set A: Even numbers.

• Set B: Multiples of 3.

Jonathan writes a whole number on a card.

• The number is between 55 and 83 inclusive.

• The square root of the number is greater than 8 but less than 9.

• The highest common factor (HCF) of 49 and the number is 7.

What number is on Jonathan’s card?

The number on Jonathan’s card is_{………........ ……………..}

Using only the numbers in the following list,

10 11 12 13 14 15 16 17 18 19 20

write down

two prime numbers that have a sum of 32,

The two numbers are_{………........ ………….} and_{………........ ………….}

a number that is a multiple of both 4 and 6,

a number that is a factor of 51.

Find the whole number that satisfies all of the following conditions.

• It is a whole number between 1 and 100 inclusive. • 10% of the number is greater than 2 but less than 8. • of the number is a square number.

• The number is not a multiple of 4.

The Venn diagram below is used for showing square numbers and even numbers.

Place the numbers 1, 2, 3, 4 and 5 in the Venn diagram.

Using only the numbers in the following list,

10 11 12 13 14 15 16 17 18 19 20

write down

two prime numbers that have a sum of 32,

The two numbers are_{………........ ………….} and_{………........ ………….}

a number that is a multiple of both 4 and 6,

a number that is a factor of 51.

Find the whole number that satisfies all of the following conditions.

• It is a whole number between 1 and 100 inclusive. • 10% of the number is greater than 2 but less than 8. • of the number is a square number.

• The number is not a multiple of 4.

The highest common factor (HCF) of 30 and 75 is the square root of a number.

What is the number?

The cube root of 32.768 is 33 % of a number.

What is the number?

The highest common factor (HCF) of 30 and 75 is the square root of a number.

What is the number?

The cube root of 32.768 is 33 % of a number.

What is the number?

Sara is in charge of a game at her school’s Christmas party.

Two fair spinners are spun as shown in the example below.

People can make a two-digit number using the numbers shown on the spinners using the following rule:

Multiply the number on the first spinner by 10 and then add the number on the second spinner.

One example, as shown above, makes the number 21, because 2 × 10 + 1 = 21.

How many different numbers can be made playing this game?

Write down all the prime numbers that can be made playing this game.

What is the probability that a person makes a prime number when playing the game

once?

Sara charges each person £1 to play the game once. Each player who makes a prime number from their spins wins £2.

How much profit would the school expect to make when 180 people play the game?

Find the answer to the following number problem.

‘(the LCM of 12, 18 and 24) ÷ (the HCF of 36 and 54)’.

Find the answer to the following number problem.

‘(the LCM of 12, 18 and 24) ÷ (the HCF of 36 and 54)’.

Write the number fifty thousand and four in figures.

Calculate £7.20 divided by 9.

Write your answer in pence.

Mair thought of two whole numbers. When she multiplied them together, the answer was 20. When she added them together, the answer was 9.

What are the two numbers that Mair thought of?

Numbers are_........ and_........

Express 700 as a product of its prime factors in index form.

(b)

Explain how this tells you that 33 554 432 is not a square number.

A whole number is written on a card.

You are given three clues to help you work out the number on the card.

Clue 1: Double the number is between 8 and 18 inclusive.

Clue 2: The number is a prime number.

Clue 3: The number is not a factor of 100.

What is the number on the card?

You must show all your working.

The number on the card is_{……........ …….}

Calculate the answer when,

‘the largest prime number that is a factor of 28’ is multiplied by

‘the smallest prime number that is factor of 15’.

Express 700 as a product of its prime factors in index form.

(b)

Explain how this tells you that 33 554 432 is not a square number.