Prime Factorization Calculator
Prime Factorization2 × 2 × 3 × 7
Is Prime?No
Prime factorization breaks a whole number down into the prime numbers that multiply together to produce it. Every integer greater than 1 has exactly one such factorization, a result known as the fundamental theorem of arithmetic. This calculator lists those prime factors with repetition and tells you whether the number itself is prime.
Formula
n = p₁ × p₂ × … × pₖ, where each pᵢ is prime
- n
- The positive integer being factored
- pᵢ
- A prime factor, listed in ascending order with repetition
How it works
- Enter any positive whole number. The calculator repeatedly divides it by the smallest prime that divides it evenly, starting at 2, until only 1 remains.
- The result lists each prime factor in ascending order, including repeats, and joins them with the multiplication sign. If the number has no smaller divisors it is reported as prime, and the number 1 returns the value 1 with no prime factors.
Worked example
Factor the number 60 into its primes.
- Divide by 2: 60 ÷ 2 = 30, then 30 ÷ 2 = 15.
- 15 is no longer divisible by 2; divide by 3: 15 ÷ 3 = 5.
- 5 is prime, so it remains. Collecting the factors gives 2 × 2 × 3 × 5.
60 = 2 × 2 × 3 × 5, and 60 is not prime.
Frequently asked questions
- How are repeated prime factors shown?
- Each prime is listed as many times as it divides the number. For example 60 is written 2 × 2 × 3 × 5 rather than using exponents, so the count of each prime is visible directly.
- What does the calculator return for the number 1?
- The number 1 has no prime factors because it is neither prime nor composite. The calculator returns the value 1 with an empty list of prime factors.
- How does prime factorization differ from listing all factors?
- Prime factorization gives only the prime building blocks multiplied together, while a full factor list includes every divisor such as 1, the number itself, and composite divisors. Use a factor calculator if you need every divisor.