To simplify a fraction, find the Greatest Common Factor (GCF) of the numerator and denominator, then divide both by it. For example, to simplify 12⁄18, the GCF is 6 — so 12 ÷ 6 = 2 and 18 ÷ 6 = 3, giving the simplified fraction 2⁄3.
Below you'll learn two reliable methods (the GCF method and repeated division), see worked examples from easy to challenging, and test yourself with interactive practice problems.
Quick Summary — Simplifying Fractions in 3 Steps
Find the GCF of the numerator and denominator (the biggest number that divides both evenly).
Divide both the numerator and denominator by that GCF.
Done! If the GCF is 1, the fraction is already in simplest form.
Can't spot the GCF? Just keep dividing both numbers by small primes (2, 3, 5…) until nothing divides evenly. You'll reach the same answer.
What Does It Mean to Simplify a Fraction?
Definition
Simplifying a fraction (also called reducing) means dividing both the numerator and denominator by their Greatest Common Factor (GCF) to produce an equivalent fraction using the smallest possible whole numbers.
To simplify a fraction, divide both the numerator (top number) and the denominator (bottom number) by their Greatest Common Factor (GCF) until no common factor remains other than 1. The result is an equivalent fraction expressed in the smallest whole numbers possible.
Key idea: Simplifying never changes the value of a fraction. The fractions 6⁄8 and 3⁄4 look different, but they represent exactly the same amount. Simplifying just makes the fraction easier to read, compare, and use in calculations.
How Do You Simplify Fractions Using the GCF Method?
The GCF method is the most direct way to simplify any fraction in a single step. Find the Greatest Common Factor of both numbers, then divide. Here's how:
1Find the GCF of the numerator and denominator
List the factors of each number and identify the largest one they share. For example, for 12⁄18: the factors of 12 are 1, 2, 3, 4, 6, 12 and the factors of 18 are 1, 2, 3, 6, 9, 18. The largest shared factor is 6. Need help? Use our GCF Calculator.
2Divide the numerator by the GCF
12 ÷ 6 = 2. This is your new numerator.
3Divide the denominator by the GCF
18 ÷ 6 = 3. This is your new denominator.
4Write the simplified fraction
The simplified fraction is 2⁄3. Since the GCF of 2 and 3 is 1, you know it's fully simplified.
1218→12 ÷ 618 ÷ 6=23
💡 Tip
The GCF method works in one step, making it ideal when you can quickly identify the GCF. For larger numbers where listing factors is harder, try the repeated division method below.
How Do You Simplify Fractions Using Repeated Division?
The repeated division method (also called successive division) works especially well with large numbers. Instead of finding the GCF upfront, you repeatedly divide both the numerator and denominator by small prime numbers until no common factor remains.
1Check if both numbers are divisible by 2
If both the numerator and denominator are even, divide each by 2. Repeat until at least one is odd.
2Check divisibility by 3, then 5, then 7…
Move to the next prime number and repeat. A number is divisible by 3 if its digit sum is divisible by 3. It's divisible by 5 if it ends in 0 or 5.
3Stop when no common prime factor remains
When you can't find any prime that divides both numbers evenly, the fraction is fully simplified.
Example — Simplify 120/180
120180→÷ 26090→÷ 23045→÷ 31015→÷ 523
We divided by 2 twice, then by 3, then by 5. The result 2⁄3 can't be reduced further because GCF(2, 3) = 1.
What Are Step-by-Step Examples of Simplifying Fractions?
Easy: Simplify 4⁄8
Step-by-step
Factors of 4: 1, 2, 4. Factors of 8: 1, 2, 4, 8. GCF = 4.
How Do You Know If a Fraction Is Already Simplified?
A fraction is already in simplest form when the numerator and denominator share no common factor other than 1 — that is, when their GCF equals 1. Here are some quick checks:
Fraction
GCF
Already Simplified?
3⁄7
1
✓ Yes
5⁄9
1
✓ Yes
8⁄12
4
✗ No → 2⁄3
11⁄13
1
✓ Yes
14⁄21
7
✗ No → 2⁄3
1⁄4
1
✓ Yes
⚡ Quick checks
Both even? Definitely not simplified — divide by 2. Numerator is 1? Always simplified (unit fractions). Both prime? Always simplified if they're different primes. One is prime? Simplified unless the other is a multiple of it.
Can You Solve These Fraction Simplification Practice Problems?
Test your understanding. Click "Show Answer" to reveal the solution and explanation for each problem.
6⁄9
2⁄3
GCF(6, 9) = 3. Divide both by 3: 6 ÷ 3 = 2, 9 ÷ 3 = 3.
10⁄25
2⁄5
GCF(10, 25) = 5. Divide both by 5: 10 ÷ 5 = 2, 25 ÷ 5 = 5.
14⁄35
2⁄5
GCF(14, 35) = 7. Divide both by 7: 14 ÷ 7 = 2, 35 ÷ 7 = 5.
24⁄36
2⁄3
GCF(24, 36) = 12. Divide both by 12: 24 ÷ 12 = 2, 36 ÷ 12 = 3.
45⁄60
3⁄4
GCF(45, 60) = 15. Divide both by 15: 45 ÷ 15 = 3, 60 ÷ 15 = 4.
56⁄72
7⁄9
GCF(56, 72) = 8. Divide both by 8: 56 ÷ 8 = 7, 72 ÷ 8 = 9.
Want to practice more? Our Simplify Fractions Calculator lets you enter any fraction and see the full solution instantly.
What Are Common Questions About Simplifying Fractions?
Simplifying a fraction means reducing it to its lowest terms by dividing both the numerator and denominator by their Greatest Common Factor (GCF). The simplified fraction has the same value as the original but uses the smallest possible whole numbers. For example, 6⁄8 simplifies to 3⁄4 because you divide both 6 and 8 by their GCF of 2.
Step 1: Find the GCF of the numerator and denominator. Step 2: Divide the numerator by the GCF. Step 3: Divide the denominator by the GCF. Step 4: Write the new fraction. For example, to simplify 12⁄18: the GCF of 12 and 18 is 6. Divide both by 6 to get 2⁄3.
The GCF (Greatest Common Factor) is the largest number that divides evenly into two or more numbers. To find it, list all factors of each number and identify the largest one they share. For example, the factors of 12 are 1, 2, 3, 4, 6, 12 and the factors of 18 are 1, 2, 3, 6, 9, 18. The largest shared factor is 6, so GCF(12, 18) = 6. You can also use our GCF Calculator for quick results.
A fraction is already in simplest form when the numerator and denominator share no common factors other than 1 — meaning their GCF is 1. For example, 3⁄7 is already simplified because the only factor 3 and 7 share is 1. Quick check: if both numbers are coprime (share no common prime factors), the fraction is fully simplified.
Yes, improper fractions (where the numerator is larger than the denominator) are simplified exactly the same way as proper fractions — find the GCF and divide both parts. For example, 15⁄10 simplifies to 3⁄2 (GCF is 5). You can optionally convert the result to a mixed number: 3⁄2 = 1 1⁄2.
No. Simplifying a fraction never changes its value. The simplified fraction and the original fraction are equivalent — they represent the exact same amount. For example, 4⁄8 and 1⁄2 are equal: both represent one-half. Simplifying only changes the numbers used to express the value.
Simplifying and reducing fractions mean exactly the same thing. Both terms describe the process of dividing the numerator and denominator by their GCF to express the fraction using the smallest possible whole numbers. "Reduce to lowest terms" and "simplify" are interchangeable in mathematics education.
Not all fractions can be simplified further. A fraction is already in its simplest form when the GCF of its numerator and denominator is 1. For example, 5⁄9 cannot be simplified because 5 and 9 share no common factors besides 1. Fractions with a prime numerator or denominator are often already simplified.
For large numbers, use the repeated division method: divide both the numerator and denominator by small primes (2, 3, 5, 7…) until no common factor remains. For example, 120⁄180: divide both by 2 → 60⁄90, divide by 2 → 30⁄45, divide by 3 → 10⁄15, divide by 5 → 2⁄3. Alternatively, use the Euclidean algorithm to find the GCF directly.
Simplifying fractions makes them easier to understand, compare, and use in further calculations. Teachers typically require answers in simplest form. Simplified fractions are also essential for finding common denominators when adding or subtracting fractions, and they reduce computational complexity in algebra and higher mathematics.
Simplify the fraction as if both numbers were positive — find the GCF and divide both parts by it. Then apply one negative sign to the result, typically placed on the numerator or in front of the fraction. For example, −12⁄18 simplifies to −2⁄3 because GCF(12, 18) = 6.
The fastest method is to recognize the GCF immediately and divide once. For quick mental math, check if both numbers are even (divide by 2), share a digit sum divisible by 3 (divide by 3), or end in 0 or 5 (divide by 5). Repeat these quick checks until no common factor remains.