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Factors, multiples and primes

Free Printable Factors, multiples and primes PDF Worksheets, Revision Guide & GCSE Past Paper Questions (Grade 1)

Download free factors, multiples and primes worksheets (PDF), GCSE maths past paper questions and worked solutions for Factors, multiples and primes (1M). This is a Grade 1 number topic from the GCSE questions by topic collection for Foundation and Higher tier GCSE Maths (Edexcel, AQA, OCR and IGCSE).

The free PDF worksheets table below brings together printable question booklets (Qs) and worked answers or mark schemes (Ans) from Maths Genie, Corbett Maths, Maths Takeaway, Dr Austin, Maths4EveryOne, Metatutor, E Classroom and PMT, along with past paper question booklets.

Below the worksheet links you can read our factors, multiples and primes revision notes and worked examples with diagrams, try real GCSE past paper factors, multiples and primes questions with step-by-step solutions, or download a PDF of all factors, multiples and primes worksheet links.

Free Factors, multiples and primes PDF Worksheets & Answers

Grade 1 • Topic 1M
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KS2 SATs questions & solutions
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GCSE topic booklet & answers
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PMT (Edxl)
Edexcel GCSE topic questions & solutions
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PMT (AQA)
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PMT (IGCSE)
Edexcel IGCSE topic questions & solutions
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Online topic notes & examples
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Grade 1 topics
1A - Addition1B - Subtraction
1C - Multiplication1D - Division
1E - Time1F - Ordering FDP
1G - Place Value1H - Rounding
1J - Negative numbers1K - Powers and roots
1L - BIDMAS1M - Factors, multiples and primes
1N - Coordinates1P - Pictograms
1Q - 2D shapes1R - 3D shapes
GCSE Maths Grade 1 Revision Notes & Method

Guide to Factors, multiples and primes: Explanation, Diagrams & Worked Examples

Download Printable One Page Guide (PDF)

Explanation:

A factor of a number divides into it exactly with no remainder. Always find factors in factor pairs starting from 1 × n so you never miss one. A multiple is a number in its times table (e.g. multiples of 6 are 6, 12, 18, 24, …).

A prime number has exactly two factors: 1 and itself. Remember that 1 is NOT prime (it only has one factor) and 2 is the only even prime number. The first ten primes are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.

Example 1: List all the factors of 24, and write down which of these factors are prime numbers.

Solution:

Find factor pairs systematically from 1 upwards:
• 1 × 24 = 24   • 2 × 12 = 24
• 3 × 8 = 24    • 4 × 6 = 24
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Prime factors: 2 and 3 (1 is not prime)

Example 2: From the list 9, 15, 17, 24, 27, 32, write down: (a) a prime number (b) a multiple of 8 (c) a factor of 45

Solution:

(a) 17 only divides by 1 and 17 → 17
(b) 8 times table: 8, 16, 24, 32 → 24 (or 32)
(c) 45 = 9 × 5 and 45 = 15 × 3 → 9 (or 15)
Answers: (a) 17  (b) 24 or 32  (c) 9 or 15
Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Factors, multiples and primes Questions & Answers

Past Paper Example 1 IGCSE Specimen 2F Q1 4 marks
Full Paper (PDF) • Mark Scheme (PDF)
From the numbers in the box, write down
6917202863
(a) the multiple of 5 [1 mark]
(b) the factor of 30 [1 mark]
(c) the square number [1 mark]
(d) the prime number [1 mark]
Worked Solution & Mark Scheme (4 marks)
Part (a) Solution:
20 = 4 × 5 B1
Answer (a): 20
Part (b) Solution:
30 ÷ 6 = 5 B1
Answer (b): 6
Part (c) Solution:
9 = 3² B1
Answer (c): 9
Part (d) Solution:
17 has only two factors, 1 and 17 B1
Answer (d): 17
Past Paper Example 2 IGCSE Jun 2021 1F Q1 5 marks
Full Paper (PDF) • Mark Scheme (PDF)
From the numbers in the box, write down
8917354880
(a) a factor of 40 [1 mark]
(b) a multiple of 7 [1 mark]
(c) a prime number [1 mark]
(d) a square number [1 mark]
(e) the two numbers with a difference of 31 [1 mark]
Worked Solution & Mark Scheme (5 marks)
Part (a) Solution:
40 ÷ 8 = 5 B1
Answer (a): 8
Part (b) Solution:
5 × 7 = 35 B1
Answer (b): 35
Part (c) Solution:
17 is prime B1
Answer (c): 17
Part (d) Solution:
3² = 9 B1
Answer (d): 9
Part (e) Solution:
48 − 17 = 31 B1
Answer (e): 17 and 48
Past Paper Example 3 AQA Jun 2025 1F Q2 4 marks
Full Paper (PDF) • Mark Scheme (PDF)
Here is a card from a game.
13328271536
(a) Write down the number from the card that is a multiple of 5 [1 mark]
(b) Write down the number from the card that is a factor of 40 [1 mark]
(c) Write down the number from the card that is a prime number. [1 mark]
(d) Write down the number from the card that is a square number. [1 mark]
Worked Solution & Mark Scheme (4 marks)
Part (a) Solution:
15 ends in 5, so multiple of 5 B1
Answer (a): Answer 15
Part (b) Solution:
40 ÷ 8 = 5, so 8 is a factor of 40 B1
Answer (b): Answer 8
Part (c) Solution:
13 has only 1 and 13 as factors, so prime B1
Answer (c): Answer 13
Part (d) Solution:
6² = 36, so 36 is a square number B1
Answer (d): Answer 36

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