Prime Factorization Calculator
Type a whole number to break it into prime factors, with the repeated-division steps you'd write in class.
- Nothing you type is stored
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Prime factorisation
2³ × 3² × 5
- Written out
- 2 × 2 × 2 × 3 × 3 × 5
- Different primes
- 3
- Total factors
- 24
Show working
- 360 ÷ 2 = 180
- 180 ÷ 2 = 90
- 90 ÷ 2 = 45
- 45 ÷ 3 = 15
- 15 ÷ 3 = 5
- 5 ÷ 5 = 1
- 360 = 2³ × 3² × 5
How to use
- Type a whole number of 2 or more.
- Read the prime factorisation in exponent form.
- Follow the division steps: divide by the smallest prime each time.
Good to know
Every whole number above 1 is either prime or a product of primes in exactly one way (the Fundamental Theorem of Arithmetic, NCERT Class 10). The division method keeps dividing by the smallest prime that fits: 360 ÷ 2 = 180, ÷ 2 = 90, ÷ 2 = 45, ÷ 3 = 15, ÷ 3 = 5, ÷ 5 = 1, so 360 = 2³ × 3² × 5.
The factor-tree method splits the number into any two factors and keeps splitting until only primes are left; the result is always the same. From the exponents you also get the number of factors: (3 + 1)(2 + 1)(1 + 1) = 24 for 360.
Prime factorisation is the basis for HCF and LCM, simplifying square and cube roots, and checking for perfect squares (all exponents even). Large numbers with big prime factors are split using Pollard's rho method, so 18-digit numbers work too.
Questions
What is the prime factorisation of 100?
2² × 5².
How do I find the prime factors of a number?
Divide by 2 as long as you can, then 3, then 5, 7, 11… until you reach 1. The divisors you used are the prime factors.
Can two numbers have the same prime factorisation?
No. Each number has exactly one prime factorisation (ignoring the order).
What is the prime factorisation of a prime number?
The number itself, e.g. 97 = 97.
Why is 1 not included?
1 is not prime, and multiplying by 1 changes nothing, so it is left out.