Prime factorization
Enter a whole number to get its prime factorization in exponent notation, along with every step of the repeated division method.
Repeated division steps:
How the repeated division method works
Divide the number by the smallest prime that divides it evenly (2, then 3, 5, 7, 11…) and repeat the operation on the quotient until you reach 1. The divisors used along the way are the prime factors. Take 360, for example: divide by 2 three times (360 → 180 → 90 → 45), by 3 twice (45 → 15 → 5) and by 5 once, so 360 = 2³ × 3² × 5.
What prime factorization is used for
It is the foundation for finding the GCF and LCM: the greatest common factor comes from multiplying the shared prime factors with the smallest exponent, while the least common multiple takes shared and non-shared factors with the largest exponent. It's also how you reduce fractions to lowest terms and count the divisors of a number (add 1 to each exponent and multiply). Fun fact: the sheer difficulty of factoring enormous numbers is what keeps RSA encryption, used by banks and websites, secure.