Simplify Fractions Calculator
Type a fraction to reduce it to its simplest form, with the greatest common factor found and divided out in front of you.
42/56 in lowest terms
3/4
42/56 simplifies to 3/4: divide the top and bottom by 14, their greatest common factor.
- Greatest common factor
- 14
- As a decimal
- 0.75
How to simplify a fraction
A fraction is in simplest form (lowest terms) when its numerator and denominator have no common factor except 1. To get there in one step, divide both by their greatest common factor (GCF). For 42/56 the GCF is 14, and 42 ÷ 14 = 3, 56 ÷ 14 = 4, so 42/56 = 3/4.
Euclid’s algorithm finds the GCF without listing factors: divide the larger number by the smaller and keep the remainder, then divide the previous divisor by that remainder, until the remainder is 0. For 56 and 42: 56 = 1 × 42 + 14, then 42 = 3 × 14 + 0, so the GCF is 14. It works just as fast for numbers with hundreds of digits.
You can also simplify in stages, dividing by any common factor you spot (both even? divide by 2; digits add up to a multiple of 3? divide by 3) and repeating. It reaches the same answer; the GCF just gets there in one go.
a/b = (a ÷ g) / (b ÷ g), where g = gcd(a, b)
- Euclid described this method of repeated subtraction to find the greatest common measure of two numbers around 300 BC, in Book VII of the Elements. Source: Euclid’s Elements, Book VII, Proposition 2 (D. E. Joyce’s edition).
- Equivalent fractions, a/b = (n × a)/(n × b), are a grade 4 standard: multiplying or dividing the top and bottom by the same number keeps the value (4.NF.A.1). Source: Common Core State Standards, Grade 4 Number and Operations: Fractions.
Fractions in simplest form
Fractions people often need to reduce, with the greatest common factor that does it in one step.
| Fraction | GCF | Simplest form | Decimal |
|---|---|---|---|
| 2/4 | 2 | 1/2 | 0.5 |
| 4/8 | 4 | 1/2 | 0.5 |
| 6/8 | 2 | 3/4 | 0.75 |
| 8/12 | 4 | 2/3 | 0.6667 |
| 9/12 | 3 | 3/4 | 0.75 |
| 10/15 | 5 | 2/3 | 0.6667 |
| 12/16 | 4 | 3/4 | 0.75 |
| 14/21 | 7 | 2/3 | 0.6667 |
| 15/20 | 5 | 3/4 | 0.75 |
| 16/24 | 8 | 2/3 | 0.6667 |
Show all 20 rowsShow fewer
| 18/24 | 6 | 3/4 | 0.75 |
| 20/25 | 5 | 4/5 | 0.8 |
| 24/36 | 12 | 2/3 | 0.6667 |
| 25/100 | 25 | 1/4 | 0.25 |
| 36/48 | 12 | 3/4 | 0.75 |
| 45/60 | 15 | 3/4 | 0.75 |
| 75/100 | 25 | 3/4 | 0.75 |
| 84/36 | 12 | 2 1/3 | 2.3333 |
| 125/1000 | 125 | 1/8 | 0.125 |
| 144/360 | 72 | 2/5 | 0.4 |
Frequently Asked Questions
How do I know a fraction is fully simplified?
When the GCF of the top and bottom is 1. A quick check: if both are even, or both end in 0 or 5, or both have digit sums divisible by 3, it can still be reduced.
Should I simplify an improper fraction to a mixed number?
Simplifying and converting are separate steps. 84/36 simplifies to 7/3, which you can leave as it is (often preferred in algebra) or write as the mixed number 2 1/3.
Can a fraction with a prime denominator be simplified?
Only if the numerator is a multiple of that prime. 6/7 is already in lowest terms, but 14/7 simplifies to 2.