Factors, Multiples and Primes Puzzle Set
Factors, multiples and primes puzzle sets test identifying factors, multiples and prime numbers, and finding the highest common factor (HCF) and lowest common multiple (LCM), applied through logic-puzzle style clues rather than bare definitions. 11+ and CEM-style papers often give several clues about a mystery number at once, so a pupil must narrow down the possibilities systematically rather than guessing.
Method
- List the factors of a number by finding every pair of numbers that multiply together to give it, working systematically from 1 upwards.
- List multiples of a number by counting up in that number, continuing as far as the question needs.
- Remember a prime number has exactly two factors, 1 and itself; 1 is not a prime number, and 2 is the only even prime number.
- To find the HCF of two numbers, list the factors of each and pick the largest number that appears in both lists.
- To find the LCM of two numbers, list multiples of each and pick the smallest number that appears in both lists.
- In puzzle-style questions, apply the clues one at a time to cross numbers off a shortlist, rather than trying to satisfy every clue in one go.
Worked example
I am thinking of a number less than 50. It is a multiple of 6, it is a factor of 72, it is also a multiple of 9, and it is greater than 20. What is the number?
- List the multiples of 6 that are less than 50: 6, 12, 18, 24, 30, 36, 42, 48.
- List the factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.
- Find the numbers common to both lists: 6, 12, 18, 24, 36.
- Keep only the multiples of 9 from this shortlist: 18 and 36.
- Apply the final clue, greater than 20: only 36 is greater than 20.
- Final answer: 36.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1List all the factors of 30.Show answer
Answer: 1, 2, 3, 5, 6, 10, 15, 30
Q2List the first five multiples of 7.Show answer
Answer: 7, 14, 21, 28, 35
Q3Is 91 a prime number? Explain your answer.Show answer
Answer: No; 91 = 7 x 13, so it has factors other than 1 and itself
Q4Find the HCF of 24 and 36.Show answer
Answer: 12
Q5Find the LCM of 8 and 12.Show answer
Answer: 24
Q6I am a two-digit number, a multiple of 4, and a factor of 60. What could I be?Show answer
Answer: 12, 20 or 60
Q7Explain why every prime number greater than 2 must be an odd number.Show answer
Answer: Any even number greater than 2 can be divided exactly by 2, as well as by 1 and itself, so it has more than two factors and cannot be prime; 2 is the only exception, since it is itself the even factor.
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
Find the HCF and LCM of 18 and 24.
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I am thinking of a number between 40 and 100. It is a multiple of 5, it is a factor of 180, the sum of its digits is 9, and it is greater than 50. What is the number?
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Free printable worksheet
Want more practice on paper? Download the factors, multiples and primes puzzle set worksheet pack - 6 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 22 of 11+ Maths Workbook 4, the whole course as one free printable PDF.
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