Factors and multiples · Usually met around P4
Highest common factor
Short division: multiply the divisors.
How to do it
Method
Short division: multiply the divisors
24, 36 → 12, 18 → 6, 9 → 2, 3: 2 × 2 × 3 = 12
Another way
Short division, or listing
Common factors of 24 and 36: 1, 2, 3, 4, 6, 12 → 12
In full
Use short division. Divide both numbers by a factor they share (try the primes 2, 3, 5, 7 first). Keep going until the two quotients share no factor except 1. Multiply the divisors to get the H.C.F. 24 and 36: ÷ 2 → 12 and 18, ÷ 2 → 6 and 9, ÷ 3 → 2 and 3. 2 and 3 share no factor except 1, and 2 × 2 = 4, 4 × 3 = 12, so the H.C.F. is 12. Another way is listing: write out all the factors of both numbers and pick the biggest one they share.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
H.C.F. of 56 and 63 = ?
Show the answer and working
Answer: H.C.F. of 56 and 63 = 7
H.C.F. of 56 and 63: by short division, 56 and 63 ÷ 7 → 8 and 9; 8 and 9 share no factor but 1, so the H.C.F. is the divisor, 7
Example 2
H.C.F. of 52 and 65 = ?
Show the answer and working
Answer: H.C.F. of 52 and 65 = 13
H.C.F. of 52 and 65: by short division, 52 and 65 ÷ 13 → 4 and 5; 4 and 5 share no factor but 1, so the H.C.F. is the divisor, 13
Example 3
H.C.F. of 12 and 18 = ?
Show the answer and working
Answer: H.C.F. of 12 and 18 = 6
H.C.F. of 12 and 18: by short division, 12 and 18 ÷ 2 → 6 and 9; 6 and 9 ÷ 3 → 2 and 3; 2 and 3 share no factor but 1. Multiply the divisors: 2 × 3 = 6, so the H.C.F. is 6
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