Reduce a fraction to its simplest form using the GCF.
Teachers and textbooks expect fractions in simplest form, and a simplify fractions calculator gets you there in one step. Enter the numerator and denominator, and it finds the greatest common factor, divides both numbers by it, and gives the fraction in lowest terms. It also shows the mixed number and the decimal, so you have every form you might need.
Quick answer: to simplify a fraction, divide the numerator and the denominator by their greatest common factor. For 18/24, the GCF is 6, so 18/24 = 3/4.
How to Use the Simplify Fractions Calculator
- Enter the numerator and the denominator as whole numbers.
- Read the simplest form, the mixed number (if the fraction is bigger than 1), the greatest common factor (GCF) used, and the decimal.
- Follow the steps to see the GCF and each division.
If your fraction has decimals in it, such as 0.5/2, convert it first with the decimal to fraction calculator.
How to Simplify a Fraction
- Find the greatest common factor of the numerator and denominator: the largest number that divides both exactly.
- Divide the numerator by the GCF.
- Divide the denominator by the GCF.
If the GCF is 1, the fraction is already in simplest form.
Simplifying Fraction Examples
84/126. The GCF of 84 and 126 is 42. 84 ÷ 42 = 2 and 126 ÷ 42 = 3, so 84/126 = 2/3.
18/24. The GCF is 6, so 18/24 = 3/4.
45/60. The GCF is 15, so 45/60 = 3/4.
150/40. The GCF is 10, so 150/40 = 15/4, which is 3 3/4 as a mixed number.
Ways to Find the GCF
- List the factors. Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. The largest one in both lists is 6.
- Use prime factors. 84 = 2² × 3 × 7 and 126 = 2 × 3² × 7. Multiply the primes they share: 2 × 3 × 7 = 42. The prime factorization calculator gives these for any number.
- Divide in small steps. Keep dividing by 2, 3 or 5 until nothing more divides both. 84/126 → 42/63 → 14/21 → 2/3. It takes longer but ends in the same place.
Finding the GCF of Large Numbers
For big numbers, Euclid’s method is fastest. Divide the larger number by the smaller, then keep dividing the last divisor by the remainder until the remainder is 0. The last divisor is the GCF.
84 and 126: 126 ÷ 84 = 1 remainder 42. Then 84 ÷ 42 = 2 remainder 0. The GCF is 42.
Mistakes to Avoid
- Stopping too early. 18/24 → 9/12 is not finished. 9 and 12 still share a factor of 3.
- Dividing only one number. Whatever you divide the top by, you must divide the bottom by too.
- Cancelling digits. 16/64 is 1/4, but not because you can cross out the 6s. That trick almost never works.
Related Fraction Tools
- To add, subtract, multiply or divide fractions, use the fraction calculator. It simplifies every answer automatically.
- To switch between mixed numbers and improper fractions, use the mixed number calculator.
- To simplify a ratio such as 24:36, use the ratio calculator.
Simplify Fractions FAQs
What does simplest form mean?
A fraction is in simplest form, or lowest terms, when the only number that divides both the numerator and the denominator is 1.
Can an improper fraction be in simplest form?
Yes. 15/4 is in simplest form, because 15 and 4 share no factor other than 1. Teachers may still ask you to write it as the mixed number 3 3/4.
Do equivalent fractions have the same simplest form?
Yes. 2/3, 4/6, 18/27 and 84/126 all simplify to 2/3.
Does simplifying change the value?
No. Dividing the top and bottom by the same number keeps the value the same. Only the numbers get smaller.
How we checked this page: each GCF was confirmed from the prime factors, and every simplified fraction matches the calculator.