Factors
Maths: Year 5 & 6 National Curriculum, topic 5.2.4
Factors
A factor is a number which divides exactly into another number without any remainders.
Example: factors of 10
- The factors of 10 are all the numbers that 10 can be divided by with no remainders.
- 1 is a factor of 10. 10 ÷ 1 = 10
- 10 is a factor of 10. 10 ÷ 10 = 1
- 2 is a factor of 10. 10 ÷ 2 = 5
- 5 is a factor of 10. 10 ÷ 5 = 2
Factors come in pairs
- Factors can be found by finding two numbers that multiply to make a number.
- E.g. 2 × 5 = 10
- 2 and 5 are both factors of 10.
- E.g. 1 × 10 = 10
- 1 and 10 are both factors of 10.
Factors come in pairs 2
- You can think of factors in pairs.
- 2 and 5 are a factor pair of 10 because 2 × 5 = 10.
- 1 and 10 are a factor pair of 10 because 1 × 10 = 10.
Factor Bugs
Factor bugs are a fun way to find all the factor pairs of a number. The legs of a factor bug show you the factor pairs.
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Find the first factor pair
- The first factor pair is always 1 and the number you're finding factors for.
- The first factor pair is 1 and 24 because 1 × 24 = 24.
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Find the next factor
- Next, work out if 2 is a factor of 24.
- 2 × 12 = 24
- So 2 and 12 is the next factor pair of 24.
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Find the next factor
- Next, work out if 3 is a factor of 24.
- 3 × 8 = 24
- So 3 and 8 is the next factor pair of 24.
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Find the next factor
- Next, work out if 4 is a factor of 24.
- 4 × 6 = 24
- So 4 and 6 is the next factor pair of 24.
Find the next factor
- Next, work out if 5 is a factor of 24.
- 5 is NOT a factor of 24 because there is no whole number that you can multiply 5 by to get 24.
- Next, work out if 6 is a factor of 24.
- You already know 6 is a factor of 24 because 4 × 6 = 24.
The factors of 24
- You know you have all the factors of a number when you reach a number that you already know is a factor (6 in this example)
- We can say that the factors of 24 are 1, 24, 2, 12, 3, 8, 4 and 6.
Test yourself on Factors
What factor of 15 pairs with 3?
What factor of 21 pairs with 7?
Which factor of 24 pairs with 6?
Is 5 a factor of 16?
Is 3 a factor of 21?