Factors, multiples and primes

Here is a card from a game.

Write down the number from the card that is a multiple of 5

Write down the number from the card that is a factor of 40

Write down the number from the card that is a prime number.

Write down the number from the card that is a square number.

Work out the highest common factor (HCF) of 16 and 24

Work out the lowest common multiple (LCM) of 10 and 15

Write 42 as a product of its prime factors.

Factorise fully 3n² + 5n + 2

A sequence has nth term 3n² + 5n + 2

Are any of the terms in the sequence a prime number? Tick a box.

Give a reason for your answer.

Write down all the factors of 20

Mica says, “When two multiples of 5 are added, the answer is always a multiple of 10”

Give one example to show that he is wrong.

A number is picked at random from the first three positive odd numbers. A number is picked at random from the first four prime numbers. The two numbers are multiplied to get a score.

Complete the table.

What is the probability that the score is a square number? Give your answer as a fraction.

At a restaurant, vegan pizzas have two different toppings. The toppings are sweetcorn (S) mushrooms (M) peppers (P)

Complete the table to list all the possible pairs of toppings.

At the restaurant, dough balls can be ordered in small portions and large portions.

A group of people want to order exactly 44 dough balls.

Show how they can do this.

A code has five different digits written in order, starting with the smallest. The last digit is the only square number. The middle digit is the only even number.

Work out the code.

a and b are different prime numbers.

Work out the value of a⁴ × b

c and d are different prime numbers.

Circle the equation for which c⁴ × d² × e is a cube number.

Work out the lowest common multiple (LCM) of 20 and 25

Put all the numbers 4, 5, 6, 10 and 20 into the grid so that the numbers in each row and each column multiply to 120

Write down all the factors of 45

The first two cube numbers are 1 and 8

Show that the 3rd cube number can be written as the sum of three different prime numbers.

The first two cube numbers are 1 and 8

Show that the 3rd cube number can be written as the sum of three different prime numbers.

Here is a list of numbers. 14 9 20 29 3 45 33

Which number in the list is a multiple of 4 ?

Which number in the list is a square number?

Which two numbers in the list have a total of 43 ?

Work out largest number in the list ÷ smallest number in the list

Two prime numbers are multiplied together. The answer is an even number between 50 and 60 Complete the calculation.

Work out the value of a. You must show your working.

Two prime numbers are multiplied together. The answer is an even number between 50 and 60 Complete the calculation.

a 2 7 2 × 3 × 5 = 600 Work out the value of a. You must show your working.

Complete the boxes using two different even numbers and two different odd numbers.

Complete the boxes using a factor of 12 and

Complete the boxes using a square number and a prime number.

Circle the number that is a multiple of 25

55 65 75 85

On a train, there are between 60 and 70 people. The ratio of adults to children is 5: 4 Work out the total number of people on the train.

Written as the product of prime factors,

and

Work out the highest common factor (HCF) of 12 600 and 14 112 Give your answer as an integer.

Written as the product of prime factors,

and

Work out the highest common factor (HCF) of 12 600 and 14 112 Give your answer as an integer.

Write down the two prime numbers between 25 and 35

Write down one cube number between 100 and 300

Event A has taken place every 4 years. Event B has taken place every 3 years. Both events took place in 2019 Work out the last year, before 2019, when both events took place.

Show that 2125 can be written as a cube number multiplied by a prime number between 10 and 20

Circle the number that is a factor of 10

7 6 5 4

Work out the multiple of 60 that is closest to 400

Work out the highest common factor (HCF) of 12 and 18

Q and R are two numbers. As a product of prime factors,

The highest common factor (HCF) of Q and R is 4056 Work out the value of a.

Work out the lowest common multiple (LCM) of Q and R.

Write 200 as a product of prime factors. Give your answer in index form.

Write 200 as a product of prime factors. Give your answer in index form.

Circle the factor of 32

16 12 3 64

Work out two numbers that are multiples of 9 and have a difference of 54

c = 2 10 × 3 × 5 6 Work out 18 c. Give your answer as a product of prime factors in index form.

Give your answer as an integer.

Work out the highest common factor (HCF) of 75 and 105

Work out the highest common factor (HCF) of 75 and 105

a and b are both prime numbers. They are each less than 20 Give an example where a + b is odd but not prime.

Work out the lowest common multiple (LCM) of 120 and 144

Work out the lowest common multiple (LCM) of 120 and 144

A spinner has five equal sections.

Write a number in each section so that the numbers are all different factors of 100

Write down all the factors of 18

Work out the lowest common multiple (LCM) of 12 and 15

Four positive whole numbers add up to 84 One of the numbers is a multiple of 17 The other three numbers are equal.

What are the four numbers?

Write down all the prime numbers between 40 and 50

Circle the lowest common multiple (LCM) of 5, 15 and 25

5 45 75 150

x is a positive integer. 35 ÷ x is a positive integer. Work out the four possible values of x.

a is a prime number. b is an even number. N = a² + ab Circle the correct statement about N.

could be always even even or odd

always prime always odd

k = n² + 9n + 1 Mo says, “ k will be a prime number for all integer values of n from 1 to 9” Show that Mo is wrong. You must show that your value of k is not prime.

Work out the lowest common multiple (LCM) of 20, 30 and 40 Circle your answer.

10 120 240 24 000

k = n² + 9n + 1 Mo says, “ k will be a prime number for all integer values of n from 1 to 9” Show that Mo is wrong. You must show that your value of k is not prime.

Which of these numbers has exactly four factors? Circle your answer.

4 8 12 16

a is a common factor of 72 and 120 b is a common multiple of 6 and 9 Work out the highest possible value of

a is a common factor of 72 and 120 b is a common multiple of 6 and 9 Work out the highest possible value of

The n th term of a sequence is 12 n – 5 Work out the numbers in the sequence that have two digits and are not prime.

n is an odd number. p is a prime number. In each part write down possible values of n and p so that

n + p is a square number.

np is a square number.

Which of these numbers has exactly two factors? Circle your answer.

6 7 8 9

Circle the highest common factor (HCF) of 6xy² and 4x³y

N is a number. As a product of prime factors in index form N = 2 × 3⁴ × y³ Work out 3N² as a product of prime factors in index form. Give your answer in terms of y.

Write 36 as a product of prime factors. Give your answer in index form.

Write 36 as a product of prime factors. Give your answer in index form.

Circle the multiple of both 8 and 12

4 32 72 108

List all the factors of 30

A factor of 30 is chosen at random. What is the probability that it is a 2-digit number?