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Break down any number into its prime factors with exponent form.

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Prime Factorization — Methods & Examples

Prime factorization is expressing a composite number as a product of prime numbers. By the Fundamental Theorem of Arithmetic, every integer greater than 1 has a unique prime factorization. It is used for finding GCF, LCM, simplifying square roots, and in cryptography.

NumberPrime FactorizationNotation
122 × 2 × 32² × 3
362 × 2 × 3 × 32² × 3²
602 × 2 × 3 × 52² × 3 × 5
1002 × 2 × 5 × 52² × 5²
3602 × 2 × 2 × 3 × 3 × 52³ × 3² × 5
How to find prime factorization by division method?
Divide the number by the smallest prime (2), then divide the quotient by the smallest prime, and so on until the quotient is 1. Example for 60: 60÷2=30, 30÷2=15, 15÷3=5, 5÷5=1. So 60 = 2² × 3 × 5.
What is the prime factorization of 72?
72÷2=36, 36÷2=18, 18÷2=9, 9÷3=3, 3÷3=1. So 72 = 2³ × 3² = 8 × 9 = 72 ✓. The prime factors are 2 and 3.
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