Prime Factorization

Any natural (positive whole) number can be written as a product of prime numbers.

The prime factorization calculator quickly and accurately breaks any natural number into a product of prime numbers, called factors.

Prime numbers up to 100:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

How to factor a number by hand

To break a number into prime factors, divide it by prime numbers. Start with the smallest one, 2, and move on to the next larger prime when needed. Keep dividing until the result of the division is 1.

Prime factorization step by step

1. Divide the number by 2 as long as it divides evenly, with no remainder and no fractional part.
2. If there is a remainder, divide by the next number in the sequence of primes.
3. Keep dividing and moving to the next prime until the quotient equals one.
4. Write down the factor every time the number divides without a remainder.

Prime factorization example:
Let's factor the number 40.

Division		Quotient
40 ÷ 2	=	20
20 ÷ 2	=	10
10 ÷ 2	=	5
5 ÷ 5	=	1

  All the factors are shown in bold. Let's write them with exponents, where the exponent is how many times the factor occurs:

Number		Factors		Exponential form
40	=	2×2×2×5	=	23 × 51