Break a number into its prime factors with exponents. Enter a whole number above 1.
Usage Tip
Start dividing by 2, then 3, 5, 7, and so on — you only need primes up to the square root, with whatever is left being prime.
Divisor count = product of (each exponent + 1)
The factorization underlies GCF, LCM, and fraction reduction.
A prime number factors to just itself.
The total divisor count comes from the exponents.
Prime factorization breaks a whole number into the prime numbers that multiply together to make it. For example, 360 equals 2 cubed times 3 squared times 5. Every whole number above 1 has exactly one prime factorization, apart from the order of the factors.
Prime factors are useful for simplifying fractions, finding the greatest common factor and least common multiple of two numbers, and checking whether a number is a perfect square, which happens when every exponent is even. A prime number has only itself as its prime factorization. Very large numbers can take a long time to factor, which is the basis of some forms of encryption.