Factors, multiples & primes

Find the lowest common multiple (LCM) of 45 and 70

Find the lowest common multiple (LCM) of 45 and 70

Lui is asked to work out the value of 30 – 4 x when x = –5

Here is his working and his answer.

Lui’s answer is wrong.

Explain what Lui has done wrong in his working.

Oni thinks of a number. She calls the number Y

Y is a positive, odd number and Y 9

Write down all the possible values of Y

Write 1400 as a product of powers of its prime factors. Show your working clearly.

A 2³ 5⁴ 7 11 B 2² 5² 7² C 2² 5³ 7⁴

Find the highest common factor (HCF) of A, B and C Write your answer as a product of prime factors.

From the numbers in the box, write down

an odd number

a multiple of 12

a prime number

a factor of 24

Here is a list of numbers.

2 8 9 18 24 28

From the numbers in the list, write down

an odd number

a number that is a multiple of both 4 and 6

a cube number

a prime number

Work out the value of

Find the highest common factor (HCF) of 72 and 108 Show your working clearly.

Find the highest common factor (HCF) of 72 and 108 Show your working clearly.

A 2⁵ 5 7² B 2³ 5³ 7⁴

Write down the highest common factor (HCF) of 5A and 2B Give your answer as a product of prime factors.

A 2⁵ 5 7² B 2³ 5³ 7⁴

Work out the value of AB² Give your answer as a product of prime factors.

Write 1400 as a product of powers of its prime factors. Show your working clearly.

A 5³ 7³ 11⁶ and B 5⁶ 7² 11⁴

Find the highest common factor (HCF) of A and B Give your answer as a product of powers of its prime factors.

Write down the prime number that lies between 90 and 100

Find the cube root of 79 507

Work out the value of 4² × 5³

Write 2250 as a product of powers of its prime factors. Show your working clearly.

Write 300 as a product of its prime factors. Show your working clearly.

A = 2 2 2 3 3 5

B = 2 2 3 3 3 5

Find the lowest common multiple (LCM) of 5A and 7B Show your working clearly.

Write 2250 as a product of powers of its prime factors. Show your working clearly.

Write 300 as a product of its prime factors. Show your working clearly.

A = 2 2 2 3 3 5

B = 2 2 3 3 3 5

Find the lowest common multiple (LCM) of 5A and 7B Show your working clearly.

Here is a list of numbers.

9 11 13 15 21 60

From the numbers in the list, write down

the even number

the square number

the multiple of 7

the factor of 30

Here is a list of numbers.

2 8 14 15 16 18 20

From this list, write down

the odd number

the multiple of 6

the square number

the prime number

two numbers with a sum of 26

Write down all the factors of 10

Find the lowest common multiple (LCM) of 18 and 60

Find the highest common factor (HCF) of 130 and 208 Show your working clearly.

Here are four cards. Each card has a number on it.

These four cards are arranged to make the number 5763

Arrange the four cards to make the smallest possible number.

Arrange the four cards to make the largest possible even number.

Arrange two of the cards to make a prime number.

Arrange two of the cards to make a multiple of 8

Find the highest common factor (HCF) of 200 and 420

A = 2³ 3 5 7² B = 2 3² 7 C = 3 5² 11

Find the lowest common multiple (LCM) of A, B and C Write your answer as a product of powers of prime factors.

Find the highest common factor (HCF) of 200 and 420

A = 2³ 3 5 7² B = 2 3² 7 C = 3 5² 11

Find the lowest common multiple (LCM) of A, B and C Write your answer as a product of powers of prime factors.

Here is a list of numbers.

3 6 7 8 11 25 27

From the numbers in the list, write down

an even number

a multiple of 9

a square number

a prime number

Use brackets to make the statement correct. You may use more than one pair of brackets in the statement.

Find the highest common factor (HCF) of 56 and 84 Show your working clearly.

Find the lowest common multiple (LCM) of 60 and 72 Show your working clearly.

Find the highest common factor (HCF) of 56 and 84 Show your working clearly.

Find the lowest common multiple (LCM) of 60 and 72 Show your working clearly.

P = 3³5²7 Q = 3²57²

Write down the highest common factor (HCF) of P and Q

P = 3³5²7 Q = 3²57²

Work out the value of P³Q Give your answer in the form 3^x5^y7^z where x, y and z are positive integers.

Write 1200 as a product of powers of its prime factors. Show your working clearly.

Write 1200 as a product of powers of its prime factors. Show your working clearly.

From the numbers in the box, write down

an even number

a multiple of 9

a prime number

Here are four cards. Each card has a number on it. The four cards are arranged to make the number 7358

Show how the four cards can be arranged to make the smallest number using all four cards.

Show how the four cards can be arranged to make a correct calculation below.

Work out the lowest common multiple (LCM) of 36 and 120

A = 5² 7⁴ 11^p B = 5^m 7^n–5 11

m, n and p are integers such that m 2 n 10 p 1

Find the highest common factor (HCF) of A and B Give your answer as a product of powers of its prime factors.

Here are four fractions.

When written as a decimal, one of these fractions will give a terminating decimal.

Write down the fraction.

Write as a mixed number in its simplest form.

Here is a list of four words that can be used to describe numbers.

Use the word from the list to complete the sentence below correctly.

Find the lowest common multiple (LCM) of 28, 42 and 63 Show your working clearly.

Prove that when the sum of the squares of any two consecutive odd numbers is divided by 8, the remainder is always 2 Show clear algebraic working.

19Write 3.6 10³ as a product of powers of its prime factors. Show your working clearly.

Write 3.6 10³ as a product of powers of its prime factors. Show your working clearly.

A sequence of shapes is made by shading squares on a square grid.

On the grid, draw Shape number 4

Complete the table.

Find the number of shaded squares in Shape number 8

Explain why no shape in the sequence is made by shading exactly 50 squares.

E = {20, 21, 22, 23, 24, 25, 26, 27, 28, 29}

A = {odd numbers} B = {multiples of 3}

List the members of the set

A B

A B

A = 2⁸3⁵11⁴ B = 2⁶311⁸

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

Find the lowest common multiple (LCM) of 2A and 3B. Give the LCM as a product of powers of its prime factors.

E = {20, 21, 22, 23, 24, 25, 26, 27, 28, 29}

A = {odd numbers} B = {multiples of 3}

List the members of the set

A B

A B

A = 2⁸×3⁵×11⁴ B = 2⁶×311⁸

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

Find the lowest common multiple (LCM) of 2A and 3B. Give the LCM as a product of powers of its prime factors.

Here is a list of numbers in a box.

From the numbers in the list, write down

a multiple of 11

a factor of 30

a square number

a prime number

two numbers whose sum is 84

A = 2³3² 5²11

Find the lowest common multiple (LCM) of A and B. Give your answer as a product of powers of prime numbers.

Prove algebraically that the product of any two odd numbers is always an odd number.

Find the lowest common multiple (LCM) of 20 and 35

A = 2 3⁴³ B = 16 3³⁷

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

Express the number A B as a product of powers of its prime factors. Give your answer in its simplest form.

A = 2 3⁴³ B = 16 3³⁷

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

Express the number A B as a product of powers of its prime factors. Give your answer in its simplest form.

find the values of n for which M = 2

Here is a list of numbers.

From this list, write down

an even number

a multiple of 3

a prime number

a cube number

Write down all the factors of 9

Find the lowest common multiple (LCM) of 15 and 70

Write 880 as a product of powers of its prime factors. Show your working clearly.

Write down the largest possible four digit number using all the digits that are in the box.

From the numbers in the circle, write down

a multiple of 6

a prime number

Find the highest common factor (HCF) of 28 and 70

Find the lowest common multiple (LCM) of 28 and 105

Find the lowest common multiple (LCM) of 28 and 105

Write in figures the number seventy thousand, two hundred and sixteen.

Write down a common factor of 20 and 30

Write down a square number that is between 20 and 40

Find the cube root of 3375

Write brackets in the following calculation so that the answer is correct.

42 – 6 ÷ 6 – 3 = 40

Here is a list of numbers 13 14 18 23 30 36 From the numbers in the list, write down

an odd number

the multiple of 4

the factor of 28

Simplify k + k + k + k

Write f as a single power of 9

Write f as a single power of 3

Write 5¹⁷ 5² as a single power of 5

Write 800 as a product of its prime factors. Show your working clearly.

E = {10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}

A = {multiples of 5} B = {even numbers}

Complete the Venn diagram for this information.

Write 5¹⁷ 5² as a single power of 5

Write 800 as a product of its prime factors. Show your working clearly.

From the numbers in the box, write down

an odd number

a multiple of 12

a square number

a prime number

Find the highest common factor (HCF) of 40 and 64

A = 2ⁿ × 3 × 5^m

Write 8 A as a product of powers of its prime factors.

E = {11, 12, 13, 14, 15, 16, 17, 18, 19, 20} A = {even numbers} B = {multiples of 3}

List the members of the set

A B

A B

A މ

Write 720 as a product of its prime factors. Show your working clearly.

Find the smallest whole number that 720 can be multiplied by to give a square number.

A = 3² 5⁴ 7 B = 3⁴ 5³ 7 11

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

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

Find the Lowest Common Multiple (LCM) of 12 and 20

Find the Highest Common Factor (HCF) of 24 and 56

E = n² + n + 5

Ali thinks that the value of E will be a prime number for any whole number value of n.

Is Ali correct? You must give a reason for your answer.

A = 3⁵ 5 7³ B = 2³ 3 7⁴

Find the Highest Common Factor (HCF) of A and B.

Find the Lowest Common Multiple (LCM) of A and B.

A = 3⁵ 5 7³ B = 2³ 3 7⁴ C = 2^p 5^q 7^U

Given that the HCF of B and C is 2³ 7 the LCM of A and C is 2⁴ 3⁵ 5² 7³

find the value of p, the value of q and the value of U.

Write down a multiple of 8 that is between 20 and 50

There is only one prime number that is an even number.

Write down this number.

Shreya says that 57 is a prime number.

Is Shreya correct? Give a reason for your answer.

Write 1782 correct to the nearest hundred.

Write the number thirty two thousand and forty five in figures.

Billy works out the answer to 2 + 5 7 He says that the answer is 49

Billy is not correct as the answer should be 37

Explain what Billy has done wrong.

Chen says,

“A prime number added to an even number always gives an odd number.”

Give an example to show that Chen is not correct.