This prime factorization calculator breaks a whole number into its prime factors and writes it in exponent form. It also tells you whether the number is prime and lists every factor, every factor pair, how many factors there are and their sum.
How prime factorization works
Every whole number greater than 1 is either prime or can be written as a product of primes in exactly one way (the fundamental theorem of arithmetic). To find it, divide by the smallest prime that goes in evenly, and repeat with the result until you reach 1.
Worked example
360 ÷ 2 = 180, ÷ 2 = 90, ÷ 2 = 45, ÷ 3 = 15, ÷ 3 = 5, ÷ 5 = 1. So 360 = 2³ × 3² × 5.
The number of factors comes from the exponents: (3 + 1) × (2 + 1) × (1 + 1) = 24 factors.
Uses of prime factorization
- Finding the greatest common factor and least common multiple of numbers.
- Simplifying fractions and square roots.
- Understanding divisibility and number patterns, and the basis of encryption systems such as RSA.
Frequently asked questions
Is 1 a prime number?
No. A prime has exactly two different factors, 1 and itself. The number 1 has only one factor.
Is 2 the only even prime?
Yes. Every other even number can be divided by 2, so it has more than two factors.
What is the difference between factors and prime factors?
Factors are all numbers that divide evenly into a number. Prime factors are only the prime ones; 12 has factors 1, 2, 3, 4, 6 and 12, but prime factors 2 and 3 (12 = 2² × 3).
How large a number can I factorize?
Up to 10 trillion (10¹³). Larger numbers can take much longer to factor, which is why big prime products are used in encryption.
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Last reviewed: October 2026.