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Prime Factorization Calculator
Prime Sentinel
Nuclear Core Factorization Analyzer
About the Prime Factorization Calculator
Prime factorisation breaks a whole number into the prime numbers that multiply to make it. It is used to find GCF and LCM and in cryptography.
How to use the Prime Factorization Calculator
- Enter a positive whole number in Integer Entry.
- Press Calculate to see its prime factors.
Formula and method
Divide repeatedly by the smallest possible prime (2, 3, 5, 7, ...) until the quotient is 1. The primes used are the prime factors.
Worked example
360 ÷ 2 = 180, ÷ 2 = 90, ÷ 2 = 45, ÷ 3 = 15, ÷ 3 = 5, ÷ 5 = 1. So 360 = 2³ × 3² × 5.
Factorising 360. 360 = 2 × 2 × 2 × 3 × 3 × 5 = 2³ × 3² × 5.
When to use the Prime Factorization Calculator
- Breaking a number into its prime building blocks for maths lessons.
- Finding the GCF or LCM by comparing prime factors.
- Checking whether a number is prime.
Common mistakes to avoid
- Stopping too early. Every factor must be a prime number.
- Treating 1 as a prime number. It is not.
Tips
- Every whole number greater than 1 has exactly one prime factorisation.
- You only need to test primes up to the square root of the number.
Frequently Asked Questions
A number greater than 1 whose only divisors are 1 and itself, such as 2, 3, 5, 7 and 11.
A whole number greater than 1 whose only factors are 1 and itself, such as 2, 3, 5, 7 and 11.
Yes. This is the fundamental theorem of arithmetic.