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Greatest Common Factor Calculator

Find the greatest common factor (GCF) — also called the greatest common divisor (GCD) — of two integers using the Euclidean algorithm. The largest number that divides both inputs evenly; used everywhere from simplifying fractions to designing tilings to cryptography.

First Number

Second Number

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Math

Prime Factorization Calculator

Decompose any positive integer into its unique product of prime numbers — the fundamental "atomic" representation that underlies divisibility, fractions, modular arithmetic, and cryptography. The result is returned as a space-separated multiplication expression.

Number

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Key differences

	Greatest Common Factor Calculator	Prime Factorization Calculator
Category	Math	Math
Inputs required	2	1
Result	Greatest Common Factor	Prime Factors
What it does	Find the greatest common factor (GCF) — also called the greatest common divisor (GCD) — of two integers using the Euclidean algorithm. The largest number that divides both inputs evenly; used everywhere from simplifying fractions to designing tilings to cryptography.	Decompose any positive integer into its unique product of prime numbers — the fundamental "atomic" representation that underlies divisibility, fractions, modular arithmetic, and cryptography. The result is returned as a space-separated multiplication expression.