GCSE · Integers, powers & roots

Factors, multiples and prime numbersExam-style questions

What a factor and a multiple are and how to keep them the right way round, how to list every factor of a number in pairs, why 1 is not prime and 2 is the only even prime, the primes up to 50, square and cube numbers on sight, and how one counter-example settles an "Is she correct?" question.

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14 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 1 Level 2 Level 3 Level 4

1
Theo is asked to write down all the factors of $64$

Here is his answer.

$1, \; 2, \; 4, \; 8, \; 8, \; 16, \; 32, \; 64$
(a) What mistake has Theo made?

(1 mark)
(b) How many factors does $64$ have?

(1 mark)
(c) Explain why a square number always has an odd number of factors.

(1 mark)
Level 4 · 3 marksTry it
2
Five raffle tickets have numbers that are all different prime numbers.
- The smallest ticket number is $3$ .
- The range of the ticket numbers is $16$ .
- The median ticket number is $11$ .
- The mean ticket number is $11$ .
What are the five ticket numbers?

(4 marks)
Level 4 · 4 marksTry it
3
$a$ is a prime number.

$b$ is a square number.

$a + b = 20$

$a \times b$ is less than $50$

Work out the values of $a$ and $b$ .

(3 marks)
Level 4 · 3 marksTry it