Factors, multiples and primes

Write down a multiple of 8 that is between 25 and 35

Find the highest common factor (HCF) of 54 and 120

Find the highest common factor (HCF) of 54 and 120

Express 250 as a product of its prime factors.

Find the lowest common multiple (LCM) of 30 and 25

Express 250 as a product of its prime factors.

Find the lowest common multiple (LCM) of 30 and 25

Write down two factors of 32

Write down the multiple of 9 that is between 20 and 30

Write down two factors of 16

Write 126 as a product of its prime factors.

Find the highest common factor (HCF) of 126 and 210

Write down the multiple of 7 that is between 30 and 40

Write 90 as a product of its prime factors.

A = 2²3 B = 23²

Write down the lowest common multiple (LCM) of A and B.

Write 90 as a product of its prime factors.

A = 2²3 B = 23²

Write down the lowest common multiple (LCM) of A and B.

Aisha was born in 1993 There was an election in the year of Aisha’s 18th birthday. There is an election every 5 years. Will there be an election in 2030? You must show how you get your answer.

Write down three prime numbers that are between 20 and 40

Find the highest common factor (HCF) of 63 and 105

Find the highest common factor (HCF) of 63 and 105

Write 156 as a product of its prime factors.

Find the highest common factor (HCF) of 156 and 130

Write 156 as a product of its prime factors.

Find the highest common factor (HCF) of 156 and 130

Write down two factors of 18

Ali buys packs of balloons and boxes of pencils. There are 30 balloons in each pack. There are 24 pencils in each box. Ali buys exactly the same number of balloons and pencils. Work out how many packs of balloons and how many boxes of pencils she could have bought. You must show all your working.

_........ packs of balloons

Ali buys packs of balloons and boxes of pencils. There are 30 balloons in each pack. There are 24 pencils in each box. Ali buys exactly the same number of balloons and pencils. Work out how many packs of balloons and how many boxes of pencils she could have bought. You must show all your working.

_........ packs of balloons

Zia has to set a 4‑digit security passcode on her phone. Each digit of the passcode is a number from 1 to 9 She can use each number more than once. Zia tells her friend Amber that the first digit is a cube number the second digit is a prime number the third digit is greater than 6 the fourth digit is an odd number. The diagram shows one possible 4‑digit passcode.

Amber is going to have one attempt at guessing Zia’s passcode. Work out the probability that Amber guesses Zia’s passcode on the first attempt.

Write down three different factors of 20

Here is a list of numbers. 20 40 60 80 100 One of these numbers is a multiple of 25 Which number?

Write 60 as a product of its prime factors.

Write 60 as a product of its prime factors.

A and B are numbers such that A = 2²×3⁴×7

Find the highest common factor (HCF) of A and B.

Find the lowest common multiple (LCM) of A and B.

A and B are numbers such that A = 2²×3⁴×7

Find the highest common factor (HCF) of A and B.

Find the lowest common multiple (LCM) of A and B.

Write down a factor of 60 that is between 8 and 14

Write 500 as a product of powers of its prime factors.

Write 500 as a product of powers of its prime factors.

Two numbers m and n are such that m is a multiple of 5 n is an even number the highest common factor (HCF) of m and n is 7 Write down a possible value for m and a possible value for n.

Here is a list of numbers. 5 11 18 22 29 From the list, write down a multiple of 3

Write 124 as a product of its prime factors.

Write 124 as a product of its prime factors.

Write down a 3 digit number that is a multiple of 5

Write down two factors of 12

Work out the lowest common multiple (LCM) of 24 and 56

Here is a list of whole numbers from 21 to 30 21 22 23 24 25 26 27 28 29 30

From the list, write down a square number.

From the list, write down a multiple of 8

Find the Highest Common Factor (HCF) of 60 and 84

Find the Lowest Common Multiple (LCM) of 24 and 40

Find the Highest Common Factor (HCF) of 60 and 84

Find the Lowest Common Multiple (LCM) of 24 and 40

Write down two factors of 35

Here is a list of numbers. 5 11 18 22 29 From the list, write down a multiple of 3

Lucy uses a code to open a lock. The code is a letter followed by a 2-digit number. The letter is L or U. The number is a prime number between 20 and 30 Write down all the possibilities for Lucy’s code.

Write 84 as a product of its prime factors.

Find the lowest common multiple (LCM) of 60 and 84

Write 84 as a product of its prime factors.

Find the lowest common multiple (LCM) of 60 and 84

Here is a list of five numbers.

Find the lowest common multiple of these five numbers.

Find the Lowest Common Multiple (LCM) of 108 and 120

Find the Lowest Common Multiple (LCM) of 108 and 120

Write down two factors of 12

Here is a list of numbers.

7 8 15 16 18 22

Write down the number from the list that is a multiple of 6

Write down a prime number that is between 20 and 30

Find the highest common factor (HCF) of 72 and 90

Find the highest common factor (HCF) of 72 and 90

Write down two factors of 15

There are some small cubes and some large cubes in a bag. The cubes are red or the cubes are yellow. The ratio of the number of small cubes to the number of large cubes is 4: 7 The ratio of the number of red cubes to the number of yellow cubes is 3: 5

Explain why the least possible number of cubes in the bag is 88

All the small cubes are yellow.

Work out the least possible number of large yellow cubes in the bag.

Write down a multiple of 8 that is between 41 and 60

The first term of a sequence of numbers is 24 The term-to-term rule of this sequence is ‘add 8’ Josie says, “No number in this sequence is in the 5 times table.”

Give an example to show that Josie is wrong.

Is 85 a number in this sequence? Give a reason for your answer.

Here is a list of numbers.

3 5 7 12 15 18 20

From the list, write down a factor of 10

Write down two prime numbers that have a sum of 32

Bert has 100 cards. There is a whole number from 1 to 100 on each card. No cards have the same number.

Bert puts a star on every card that has a multiple of 3 on it. He puts a circle on every card that has a multiple of 5 on it.

Work out how many cards have both a star and a circle on them.

The diagram shows a solid metal cuboid.

The areas of three of the faces are marked on the diagram. The lengths, in cm, of the edges of the cuboid are whole numbers.

The metal cuboid is melted and made into cubes. Each of the cubes has sides of length 2.5 cm.

Work out the greatest number of these cubes that can be made.

Write down the first even multiple of 7

Write down an example to show that each of the following two statements is not correct.

The factors of an even number are always even.

All the digits in odd numbers are odd.

Margaret is thinking of a number. She says, “My number is odd. It is a factor of 36 and a multiple of 3”

There are two possible numbers Margaret can be thinking of.

Write down these two numbers.

Write down all the prime numbers between 20 and 30

Catherine says, “2 is the only even prime number.”

Is Catherine right? You must give a reason for your answer.

Find the lowest common multiple (LCM) of 40 and 56

A = 2³ 3 5
B = 2² 3 5²

Write down the highest common factor (HCF) of A and B.

Find the lowest common multiple (LCM) of 40 and 56

A = 2³ 3 5
B = 2² 3 5²

Write down the highest common factor (HCF) of A and B.

Write down all the factors of 30

Here are three lamps.

Lamp A flashes every 20 seconds. Lamp B flashes every 45 seconds. Lamp C flashes every 120 seconds.

The three lamps start flashing at the same time.

How many times in one hour will the three lamps flash at the same time?

Write 36 as a product of its prime factors.

Write 36 as a product of its prime factors.

Write down a multiple of 6 that is between 40 and 50

Steve says,

“There are more prime numbers between 20 and 30 than there are between 10 and 20”

Is Steve right? You must show how you get your answer.

a and b are odd numbers.

Give an example to show that the value of 2(a + b) is a multiple of 4

Show that, when a and b are both odd numbers, the value of 2(a + b) will always be a multiple of 4

Write down all the factors of 18

Nidah writes down two different prime numbers.

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

Find two prime numbers that Nidah could have written down.

Express 56 as the product of its prime factors.