Simplify Fractions Calculator

Enter a numerator and a denominator to reduce the fraction to its simplest form, with the GCF and the steps shown.

Examples:24/3648/18084/12617/31

48/180 = 4/15

Divide by the GCF

GCF(48, 180) = 12

  • 48 ÷ 12 = 4
  • 180 ÷ 12 = 15

Prime factorizations

48 = 243

180 = 22325

Euclidean algorithm

  1. 180 = 3 × 48 + 36
  2. 48 = 1 × 36 + 12
  3. 36 = 3 × 12 + 0

The last non-zero remainder is the GCF.

Decimal: ≈ 0.2667

What Does It Mean to Simplify a Fraction?

To simplify a fraction means to write it with the smallest whole numbers possible, without changing its value. 24/36 and 2/3 are the same amount, but 2/3 is the simplest form because 2 and 3 have no common factor except 1.

How to Use This Simplify Fractions Calculator

  1. Type the numerator (top number) into the first box.
  2. Type the denominator (bottom number) into the second box.
  3. Press Calculate to see the simplest form, the GCF and the steps behind it.

How to Simplify a Fraction Step by Step

  1. Find the GCF (greatest common factor) of the top and bottom numbers.
  2. Divide the numerator by the GCF.
  3. Divide the denominator by the same GCF.
  4. If the GCF is 1, the fraction is already in simplest form.
Handwritten notebook page simplifying 24/36: the GCF of 24 and 36 is 12, so 24/36 = 2/3
GCF(24, 36) = 12, so 24 ÷ 12 = 2 and 36 ÷ 12 = 3. That gives 24/36 = 2/3.

Why the Greatest Common Factor Matters

You could divide 24/36 by 2 and get 12/18, then by 6 and get 2/3. That works, but it takes several steps. Dividing by the GCF does the whole job in one go, and you know you are done because nothing is left to cancel.

A Fraction That Cannot Be Simplified

If the GCF is 1, the numbers are coprime and the fraction is already in simplest form. 17/31 is one of them, because 17 and 31 are both prime and share nothing.

Handwritten notebook page showing 17/31 is already in simplest form because 17 and 31 are both prime
17 and 31 are both prime, so GCF(17, 31) = 1 and 17/31 is already in simplest form.

Worked Examples

Common mistakes

Simplify Fractions FAQs

How do you simplify a fraction?

Find the greatest common factor (GCF) of the numerator and denominator, then divide both by it. For 24/36 the GCF is 12, so 24 ÷ 12 = 2 and 36 ÷ 12 = 3, giving 2/3.

How do you know when a fraction is in simplest form?

A fraction is in simplest form when the GCF of the top and bottom numbers is 1. That means no whole number except 1 divides both of them.

What is the difference between simplifying and reducing a fraction?

Nothing. "Simplify", "reduce" and "write in lowest terms" all mean dividing the numerator and denominator by their GCF so the value stays the same.

Can every fraction be simplified?

No. If the numerator and denominator are coprime, meaning their GCF is 1, the fraction is already in simplest form. 17/31 is an example.

What is 48/180 in simplest form?

4/15. The GCF of 48 and 180 is 12, and 48 ÷ 12 = 4 while 180 ÷ 12 = 15.

How do you simplify a fraction with big numbers?

Use the Euclidean algorithm to find the GCF quickly: divide the bigger number by the smaller, then the smaller by the remainder, and repeat until the remainder is 0. The last non-zero remainder is the GCF.

Does simplifying change the value of a fraction?

No. Dividing the top and bottom by the same number is the same as dividing by 1, so 24/36 and 2/3 are equal and have the same decimal value.

How do I simplify an improper fraction?

Simplify it the same way, using the GCF. If you want a mixed number, divide the numerator by the denominator and keep the remainder over the denominator.

More Worked Examples

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