This prime factorization calculator breaks a whole number down into the prime numbers that multiply together to make it. Primes are the building blocks of every whole number, the values like 2, 3, 5 and 7 that cannot be divided evenly by anything except themselves and one. Every other whole number can be written as a unique product of these primes, a fact known as the fundamental theorem of arithmetic. You enter a number and the calculator shows its factorization two ways: as a full product such as 2 times 2 times 3 times 5, and in the tidier exponent form such as 2 squared times 3 times 5. Prime factorization is a core school maths skill, and it is the practical first step for simplifying fractions, reducing surds, and finding the greatest common divisor or lowest common multiple of two numbers. It also underpins areas of number theory and the cryptography that secures online banking and messaging. The calculator uses trial division by successive primes, which is fast for everyday numbers; very large numbers with big prime factors take longer to break down, which is exactly what makes them useful in encryption. Enter any whole number from 2 upward to see its prime factors instantly.
Works on whole numbers of 2 or more. Very large numbers may take a moment. Results are exact.
The calculator divides the number by the smallest prime that goes into it, records that prime, and repeats with the result. It tries 2 first, then odd numbers upward, only needing to test up to the square root of what remains. Whatever is left at the end, if greater than one, is itself a prime factor.
Take 60. It divides by 2 to give 30, by 2 again to give 15, by 3 to give 5, and 5 is prime. So 60 is 2 times 2 times 3 times 5, written 2 squared times 3 times 5.
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