Stage 7 · Factors & multiples
Simplifying fractions
Divide top and bottom by the H.C.F.
How to do it
Method
Divide top and bottom by the H.C.F.
1218 = 23, both ÷ 6
Another way
Step by step
1218 = 69 = 23
In full
Simplifying divides the top and the bottom by the same number; the fraction's size doesn't change. Quickest is to divide once by their highest common factor (H.C.F.): 1218 — the H.C.F. of 12 and 18 is 6, 12 ÷ 6 = 2, 18 ÷ 6 = 3, so 1218 = 23. Short division finds the H.C.F. Or simplify in steps: ÷ 2 → 69, then ÷ 3 → 23, until the top and bottom share no factor but 1 — simplest form, the same answer.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
28 = ?
Answer in simplest form
Show the answer and working
Answer: 28 = 14
28: the H.C.F. of 2 and 8 is 2, 2 ÷ 2 = 1, 8 ÷ 2 = 4 → 14
Example 2
444 = ?
Answer in simplest form
Show the answer and working
Answer: 444 = 111
444: the H.C.F. of 4 and 44 is 4, 4 ÷ 4 = 1, 44 ÷ 4 = 11 → 111
Example 3
2024 = ?
Answer in simplest form
Show the answer and working
Answer: 2024 = 56
2024: the H.C.F. of 20 and 24 is 4, 20 ÷ 4 = 5, 24 ÷ 4 = 6 → 56
Example 4
2560 = ?
Answer in simplest form
Show the answer and working
Answer: 2560 = 512
2560: the H.C.F. of 25 and 60 is 5, 25 ÷ 5 = 5, 60 ÷ 5 = 12 → 512
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