Prime Factorization Calculator
Find the prime factorization of any whole number in exponent form, with the division ladder, all divisors, divisor count and simplified square root.
Prime factorization writes a whole number as a product of prime numbers, such as 360 = 2³ × 3² × 5. It is the starting point for simplifying fractions and square roots and for finding the GCF or LCM of two numbers. Enter any whole number up to 9,007,199,254,740,991 to get its prime factors, the division ladder, its divisors and its simplified square root.
How to use this tool
- Enter a whole number of 2 or more.
- Read the prime factorization in exponent form, plus the expanded product.
- Check whether the number is prime and how many divisors it has.
- Follow the division ladder in the table, which divides by the smallest prime at each step.
Formula
n = p₁^e₁ × p₂^e₂ × … × pₖ^eₖ
Every whole number above 1 has exactly one such factorization (the fundamental theorem of arithmetic). From it: number of divisors = (e₁ + 1)(e₂ + 1)…(eₖ + 1), and sum of divisors = Π (pᵢ^(eᵢ+1) − 1) ÷ (pᵢ − 1). The calculator divides by 2, 3 and then candidates of the form 6k ± 1 up to √n.
Example
360: 360 ÷ 2 = 180, 180 ÷ 2 = 90, 90 ÷ 2 = 45, 45 ÷ 3 = 15, 15 ÷ 3 = 5, and 5 is prime. So 360 = 2³ × 3² × 5. It has (3 + 1)(2 + 1)(1 + 1) = 24 divisors, which add up to 15 × 13 × 6 = 1,170, and √360 simplifies to 6√10 because 360 = 6² × 10.
Frequently asked questions
Is 1 a prime number?
No. A prime has exactly two divisors, 1 and itself, and 1 has only one. Excluding it is what keeps every factorization unique.
How do I find the GCF or LCM from prime factors?
Factor both numbers. The GCF multiplies the shared primes at their smaller power; the LCM multiplies every prime at its larger power. With 360 = 2³ × 3² × 5 and 84 = 2² × 3 × 7, the GCF is 2² × 3 = 12 and the LCM is 2³ × 3² × 5 × 7 = 2,520.
How large a number can I factor?
Up to 2⁵³ − 1 = 9,007,199,254,740,991, the largest whole number a browser stores exactly; that number itself is 6361 × 69431 × 20394401. A large prime near the limit takes a moment, because every candidate up to its square root (about 95 million) has to be ruled out.
Last updated: 2026-10-30