Factors, Multiples, Primes and Squares
Factors, multiples, primes and squares is the Year 5 number topic where pupils move beyond calculating and start describing the structure of numbers.
Before you start
Make sure you're comfortable with these topics first:
Method
- To find all the factors of a number, test each whole number from 1 upwards, checking whether it divides in exactly with no remainder; factors always come in pairs that multiply together to give the original number.
- Stop testing once the two numbers in a pair meet or cross each other (for 36 you can stop after checking up to 6, since 6 x 6 = 36), which shows every factor has been found.
- To find multiples of a number, count up in that number's times table (skip counting); a multiple of a number is always somewhere in that number's times table, however far along.
- To find common factors or common multiples of two numbers, list the factors or multiples of each number separately, then pick out the values that appear in both lists.
- To test whether a number is prime, check whether it has exactly two factors, 1 and itself; if any other whole number divides in exactly, it is not prime. Remember 1 is not prime, and 2 is the only even prime number.
- To square a number, multiply it by itself (5 squared = 5 x 5 = 25); to cube a number, multiply it by itself and then by itself again (5 cubed = 5 x 5 x 5 = 125).
- Learn the square numbers up to 12 squared (144) and the prime numbers up to 19 by heart, since SATs papers expect instant recall rather than working them out under time pressure.
Worked example
Find all the factor pairs of 48, then state whether 48 is prime, square, or neither. Then work out 6 squared and 4 cubed.
- Test whole numbers in order from 1: 1 x 48 = 48, 2 x 24 = 48, 3 x 16 = 48, 4 x 12 = 48, and 6 x 8 = 48 are all factor pairs (5 and 7 do not divide into 48 exactly, so they are skipped).
- The next number to test after 6 is 7, which does not divide in exactly, and testing can stop there since the pairs have started to repeat (8 has already appeared) - every factor pair has now been found: 1 and 48, 2 and 24, 3 and 16, 4 and 12, 6 and 8.
- 48 has more than two factors, so it is not prime; no whole number multiplied by itself gives exactly 48 (6 x 6 = 36 and 7 x 7 = 49), so 48 is not a square number either - it is simply a composite number.
- 6 squared = 6 x 6 = 36.
- 4 cubed = 4 x 4 x 4 = 64.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1List all the factor pairs of 60.Show answer
Answer: 1 x 60, 2 x 30, 3 x 20, 4 x 15, 5 x 12 and 6 x 10
Q2Write the first five multiples of 9.Show answer
Answer: 9, 18, 27, 36, 45
Q3Find the common factors of 18 and 24.Show answer
Answer: 1, 2, 3 and 6
Q4Is 51 a prime number? Explain your answer.Show answer
Answer: No, because 51 = 3 x 17, so it has factors other than 1 and 51
Q5Work out 9 squared.Show answer
Answer: 81
Q6Work out 3 cubed.Show answer
Answer: 27
Q7Find the lowest common multiple of 4 and 6.Show answer
Answer: 12
Exam-style questions
Written in the style of a KS2 Maths exam paper, with a full mark scheme.
Rosa says that 35 is a prime number because it is odd. Explain why Rosa is wrong, then write down the factor pairs of 35.
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A square number and a cube number are both greater than 20 and less than 50. The square number is even. The cube number is odd. Find the square number and the cube number, showing which square and cube numbers you checked.
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The number 91 is not prime. Find a factor of 91 that is not 1 or 91, and use it to write 91 as a multiplication of two factors.
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Free printable worksheet
Want more practice on paper? Download the factors, multiples, primes and squares 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.
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