Simplify fractions calculator
Reduce a fraction or mixed number to lowest terms. You'll see the greatest common factor, how it was found, and what the fraction looks like before and after.
- Find the GCF of 24 and 36: it is 12.
- Divide the numerator and denominator by 12.
24 ÷ 12 = 2, 36 ÷ 12 = 3 - 2/3 can't be reduced further, because 2 and 3 share no factor except 1.
Finding the GCF without listing factors
Euclid's algorithm (about 300 BC, from his Elements) says: the GCF of two numbers is also the GCF of the smaller number and the remainder. Keep dividing until the remainder is 0 — the last divisor is the GCF.
| Divide | Result |
|---|---|
| 36 ÷ 24 | 1 remainder 12 |
| 24 ÷ 12 | 2 remainder 0 |
Remainder hit 0, so GCF(24, 36) = 12.
How to simplify fractions
- Find the greatest common factor of the top and bottom — list factors for small numbers, use prime factors or Euclid's algorithm for big ones.
- Divide both by the GCF.
- Check: if the new top and bottom still share a factor, you didn't use the greatest one.
Quick divisibility checks
- 2: the last digit is even.
- 3: the digits add up to a multiple of 3 (126 → 1+2+6 = 9).
- 5: ends in 0 or 5.
- 9: the digits add up to a multiple of 9.
- 10: ends in 0 — cross off a zero from top and bottom.
Simplifying never changes the value, only the names of the pieces: 24/36 and 2/3 are equivalent fractions. For GCF and LCM of any list of numbers, use the GCF calculator.
Questions people ask
How do you simplify a fraction?
Find the greatest common factor (GCF) of the numerator and denominator and divide both by it. 24/36: the GCF is 12, so 24/36 = 2/3.
What does "simplest form" or "lowest terms" mean?
A fraction is in simplest form when the numerator and denominator have no common factor other than 1. 2/3 is in lowest terms; 4/6 is not.
Can I simplify in several small steps?
Yes. Dividing by 2, then 2 again, then 3 gets to the same place as dividing by the GCF once. It just takes more steps: 24/36 → 12/18 → 6/9 → 2/3.
How do you simplify an improper fraction?
Simplify it the same way (18/12 = 3/2), then optionally write it as a mixed number: 1 1/2.
How do you simplify a mixed number?
Leave the whole number alone and simplify the fraction part: 3 6/8 = 3 3/4.