The GCF Method (Recommended)
Divide the numerator and the denominator by their Greatest Common Factor and you're done in one step:
GCF of 24 and 36 = 12
24 ÷ 12 = 2
36 ÷ 12 = 3
Result: 2/3
GCF of 18 and 24 = 6
18 ÷ 6 = 3
24 ÷ 6 = 4
Result: 3/4
Finding the GCF Quickly
The simplest approach: list out the factors of each number, then pick the biggest one they have in common.
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
Factors of 45: 1, 3, 5, 9, 15, 45
GCF = 15
Step-by-Step Division Method
Can't spot the GCF right away? Divide by small prime numbers repeatedly until nothing else divides evenly:
÷ 2: 24/36
÷ 2: 12/18
÷ 2: 6/9
÷ 3: 2/3 ← No more common factors
Result: 2/3
When is a Fraction Already Simplified?
A fraction sits in lowest terms once the GCF of its numerator and denominator equals 1, a pair mathematicians call "coprime." Quick test: if both numbers are odd, try dividing by 3, 5, or 7. If one is even and the other odd, 2 won't divide both, so just check the odd prime factors.
GCF(7, 11) = 1 (both are prime) → Yes, already simplified
Is 9/15 in lowest terms?
GCF(9, 15) = 3 → No. Simplified: 3/5
Simplifying with Variables (Algebraic Fractions)
The same logic carries over directly - cancel out whatever factors the numerator and denominator share:
= (12/8) × (x²/x) × (y/y²)
= (3/2) × x × (1/y)
= 3x / 2y
Common Mistakes
| Mistake | Wrong | Correct |
|---|---|---|
| Only dividing one part | 6/10 → 3/10 | 6/10 → 3/5 |
| Dividing by a non-factor | 7/10 ÷ 2 = 3.5/5 | 7/10 is already simplified |
| Stopping too early | 12/18 → 6/9 | 12/18 → 2/3 |
Using the GCF Calculator
The SolverCalc GCF & LCM calculator finds the Greatest Common Factor instantly and shows a Venn diagram of the prime factors behind it. Run any fraction through it and get the simplified version in a single step.