Prime Factors Calculator

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An online calculator to factor positive integers into prime factors.

Unique Prime Factorisation Theorem

Any integer greater than zero is either a prime number or it can be represented as a product of prime numbers in a unique way.
Example
Write the prime factorization of n = 120.
Successive divisions of n by the prime numbers 2, 3, 5, 7, 11, 13, ...gives
\( \dfrac{120}{\color{red}2} = 60 \)
\( \dfrac{60}{\color{red}2} = 30 \)
\( \dfrac{30}{\color{red}2} = 15 \)
\( \dfrac{15}{\color{red}{3}} = 5 \)
\(\dfrac{5}{\color{red}{5}} = 1 \)
Hence the prime factorization of \( 120 \) is
\( 120 = 2 \times 2 \times 2 \times 3 \times 5 \)
Hence \( 120 = 2^3 \times 3 \times 5 \)

Use the calculator to Prime Factor a Number

1 - Enter a positive integer n and press "Factor". The steps in simplifying the square root are listed below.

Enter Positive Integer n =
Solution



More References and Links

Prime Factorization
Square Root
factors and multiples.