GCF Calculator: Greatest Common Factor of Two or More Numbers (with Steps)
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The GCF of 48, 180 and 72 is 12. Find it by taking each shared prime with its smallest power, or with the Euclidean algorithm.
The greatest common factor (GCF) of 48, 180 and 72 is 12. It is the largest whole number that divides every one of them without a remainder.
Prime factorization of each number
| Number | Prime factors | Divided by GCF |
|---|---|---|
| 48 | 2^4 × 3 | 4 |
| 180 | 2^2 × 3^2 × 5 | 15 |
| 72 | 2^3 × 3^2 | 6 |
Common factors
| Factor |
|---|
| 1 |
| 2 |
| 3 |
| 4 |
| 6 |
| 12 |
Every common factor of the numbers divides the GCF.
Show the steps
- Prime factorizations: 48 = 2^4 × 3; 180 = 2^2 × 3^2 × 5; 72 = 2^3 × 3^2.
- Take each prime that appears in every number, with its smallest power: 2^2 × 3 = 12.
- Euclid check for 48 and 180: 180 = 3 × 48 + 36; 48 = 1 × 36 + 12; 36 = 3 × 12 + 0. The last nonzero remainder is 12.
Greatest common factor
GCF(a, b) = GCF(b, a mod b), repeated until the remainder is 0
GCF(a, b, c) = GCF(GCF(a, b), c)
GCF × LCM = a × b (for two numbers)
- The GCF is also called the greatest common divisor (GCD) or highest common factor (HCF).
Estimates for planning and learning, not financial, tax, legal or medical advice. Check figures with your lender, tax preparer or doctor before you act.
About this calculator
The greatest common factor (GCF) of a set of numbers is the largest whole number that divides all of them with no remainder. It is also called the greatest common divisor (GCD) or highest common factor (HCF). You use it to simplify fractions, split things into equal groups and factor expressions.
Type your numbers separated by commas or spaces. The calculator shows the GCF, the prime factorization of each number, every common factor, and the steps of the Euclidean algorithm, so you can check your homework as well as get the answer.
How to use it
- Type two or more whole numbers, separated by commas or spaces.
- Read the GCF in the green box. The table shows each prime factorization and every common factor.
- Open Show the steps to see the prime factor method and the Euclidean algorithm.
Two ways to find the GCF
Prime factorization. Write each number as a product of primes. Keep the primes that appear in every number, each with its smallest exponent, and multiply them. For 48 = 24 × 3 and 180 = 22 × 32 × 5, the shared part is 22 × 3 = 12.
Euclidean algorithm. Divide the larger number by the smaller one and keep the remainder. Replace the larger number by the smaller and the smaller by the remainder. Stop when the remainder is 0. The last nonzero remainder is the GCF. It is fast even for very large numbers.
GCF and LCM
For two numbers, GCF × LCM = the product of the numbers. If you know one of them, you can find the other. See the LCM calculator for the least common multiple.
Sources
Quick check: test yourself
What is the GCF of 25 and 35?
Correct answer: 5. Both numbers are multiples of 5, and 5 and 7 share no factor.
The GCF of two numbers is 1. What are the numbers called?
Correct answer: Relatively prime. Numbers whose only common factor is 1 are relatively prime, or coprime.
Which is always true for the GCF of 18 and 30?
Correct answer: It divides both numbers. GCF(18, 30) = 6, which divides 18 and 30.
Pick an answer for each question.
Common questions
What is the GCF of two numbers?
It is the largest whole number that divides both of them evenly. For 12 and 18 it is 6.
Is GCF the same as GCD?
Yes. GCF, GCD and HCF are three names for the same number.
How do I find the GCF of three numbers?
Find the GCF of the first two, then find the GCF of that answer and the third number. Or take the shared primes of all three with their smallest exponents.
What if the GCF is 1?
The numbers are relatively prime (coprime). Fractions made from them are already in lowest terms.
How is the GCF used to simplify a fraction?
Divide the top and bottom by their GCF. For 18/30, the GCF is 6, so the fraction simplifies to 3/5.
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