Simplify 24/36
The fraction 24/36 reduced to lowest terms — two complete methods.
Method 1 — GCD (Euclidean algorithm)
Divide both numerator and denominator by their GCD (Greatest Common Divisor). We compute GCD(24, 36) using the Euclidean algorithm.
| Step 1 | 24 = 36 × 0 + 24 | |
| Step 2 | 36 = 24 × 1 + 12 | |
| Step 3 | 24 = 12 × 2 + 0 | → GCD = 12 |
Divide both terms by GCD = 12:
36 ÷ 12 = 3
Method 2 — Step-by-step (prime division)
Repeatedly divide both numerator and denominator by the smallest prime that divides both, until no common factor remains.
| ÷ 2 | 24/36 → 12/18 |
| ÷ 2 | 12/18 → 6/9 |
| ÷ 3 | 6/9 → 2/3 |
No more common factors — the fraction is fully simplified.
How to simplify a fraction
What does "simplifying a fraction" mean?
A fraction a/b is in its lowest terms (simplest form) when the numerator and denominator share no common factor other than 1 — that is, when GCD(a, b) = 1. Simplifying means dividing both a and b by their GCD.
Method 1 — the GCD approach
Compute GCD(a, b) using the Euclidean algorithm (very efficient even for large numbers), then divide: result = (a ÷ GCD) / (b ÷ GCD). This gives the answer in one step. Use the GCD calculator for a detailed breakdown.
Method 2 — step-by-step prime division
Try dividing both numerator and denominator by the smallest prime (2), repeat until 2 no longer divides both, then try 3, then 5, etc. This method reveals the prime structure of the common factors and is easy to do by hand. It is equivalent to factoring the GCD and dividing one prime at a time.
Frequently asked questions
How do you simplify a fraction step by step?
Step 1: find the GCD of the numerator and denominator (e.g. using the Euclidean algorithm). Step 2: divide both by the GCD. For example, 12/8 — GCD(12,8)=4, so 12÷4=3 and 8÷4=2, giving 3/2.
What is a fraction in lowest terms?
A fraction is in lowest terms (or simplest form, or irreducible) when its numerator and denominator share no common factor other than 1, i.e. GCD = 1. Examples: 3/2, 5/7, and 11/4 are all in lowest terms; 4/6 is not (GCD=2, simplifies to 2/3).
What is the Euclidean algorithm?
The Euclidean algorithm computes GCD(a, b) by the identity GCD(a,b) = GCD(b, a mod b), applied repeatedly until the remainder is 0. It is very fast — even for numbers in the billions, it needs only a dozen steps or so.
Can every fraction be simplified?
Every fraction can be reduced to its lowest terms, but some are already irreducible (GCD=1). For example, 7/3, 5/8, and 11/13 cannot be simplified further because their numerator and denominator share no common factor.
What if the numerator is larger than the denominator?
This tool handles improper fractions (a > b) the same way. For example, 18/4: GCD(18,4)=2, so it simplifies to 9/2. The fraction 9/2 is an improper fraction in lowest terms.