Prime Factorization Calculator

Q: What is the prime factorization of 60?

60 = 2² × 3 × 5. Divide step by step: 60 ÷ 2 = 30, 30 ÷ 2 = 15, 15 ÷ 3 = 5, 5 ÷ 5 = 1.

Q: What is the prime factorization of 100?

100 = 2² × 5². Divide step by step: 100 ÷ 2 = 50, 50 ÷ 2 = 25, 25 ÷ 5 = 5, 5 ÷ 5 = 1.

Q: Is 1 a prime number?

No, 1 is not a prime number. A prime must have exactly two distinct factors (1 and itself). Since 1 has only one factor, it is neither prime nor composite.

Find all prime factors of any number with step-by-step division, exponential form, and a list of all factors.

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What is Prime Factorization?

Prime factorization expresses any integer greater than 1 as a product of prime numbers. Every number has a unique prime factorization — this is the Fundamental Theorem of Arithmetic. For example: 360 = 2³ × 3² × 5.

How to Find Prime Factors

Divide the number by the smallest prime (2) repeatedly. Then try 3, 5, 7, 11... until the quotient is 1. The divisors are the prime factors.

Frequently Asked Questions

What is the prime factorization of 60?

60 = 2² × 3 × 5. Step by step: 60 ÷ 2 = 30, 30 ÷ 2 = 15, 15 ÷ 3 = 5, 5 ÷ 5 = 1.

What is the prime factorization of 100?

100 = 2² × 5². Step by step: 100 ÷ 2 = 50, 50 ÷ 2 = 25, 25 ÷ 5 = 5, 5 ÷ 5 = 1.

Is 1 a prime number?

No. A prime must have exactly two distinct factors (1 and itself). Since 1 has only one factor, it is neither prime nor composite.