How to Simplify Fractions: A Step-by-Step Guide
Updated · By the SolverCalc team
Quick answer
Divide the numerator and denominator by their greatest common factor (GCF).
A fraction is in simplest form when the top and bottom share no common factor other than 1. Simplifying makes answers cleaner and easier to compare. Teachers usually expect final answers in lowest terms, so this skill is worth mastering.
Method 1: divide by the greatest common factor
- List the factors of both numbers, or use prime factorization.
- Find the largest factor they share—the GCF.
- Divide the numerator and the denominator by the GCF.
Example: simplify 18/24. Factors of 18 are 1, 2, 3, 6, 9, 18. Factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. The GCF is 6, so 18/24 = (18 ÷ 6)/(24 ÷ 6) = 3/4.
Method 2: divide in smaller steps
If you cannot spot the GCF right away, divide by any common factor and repeat. For 36/48: both are even, so divide by 2 to get 18/24. Divide by 2 again: 9/12. Both are divisible by 3: 3/4. No common factor remains, so 3/4 is the simplest form.
Method 3: the Euclidean algorithm for big numbers
For large numbers, find the GCF by repeated division. To simplify 84/126: 126 = 1 × 84 + 42, then 84 = 2 × 42 + 0. The last non-zero remainder, 42, is the GCF. So 84/126 = 2/3.
Practice problems with answers
| Fraction | GCF | Simplest form |
|---|---|---|
| 18/24 | 6 | 3/4 |
| 36/48 | 12 | 3/4 |
| 45/75 | 15 | 3/5 |
| 84/126 | 42 | 2/3 |
| 14/21 | 7 | 2/3 |
Helpful divisibility rules
- Divisible by 2: the last digit is even.
- Divisible by 3: the digits add up to a multiple of 3.
- Divisible by 5: the last digit is 0 or 5.
- Divisible by 10: the last digit is 0.
To confirm your work, divide both fractions on a calculator. 45 ÷ 75 and 3 ÷ 5 both equal 0.6, so the simplification is correct.
Why simplest form matters
Simplified fractions are easier to read, compare and use in later steps. It is much clearer that 3/4 is larger than 2/3 than it is to compare 36/48 with 84/126, even though those pairs are equal.