Factor Calculator

Type a number to see all its factors, factor pairs and prime factorization instantly.

Find every factor of a whole number, plus its prime factorization and factor pairs.

Number

How to find the factors of a number

A factor of a number is a whole number that divides it exactly, with no remainder. The factors of 12 are 1, 2, 3, 4, 6 and 12, because each of them goes into 12 evenly. Every number has at least two factors, 1 and itself; a number with only those two is a prime number.

Method

Test each whole number from 1 up to the square root of the number. Whenever one divides evenly, you have found a factor and its partner: for 36, 1 pairs with 36, 2 with 18, 3 with 12, 4 with 9 and 6 with 6. Stopping at the square root is enough because every larger factor is the partner of a smaller one. This calculator does exactly that, so it finds all the factors of numbers up to 10 trillion in a moment.

Prime factorization

The prime factorization writes a number as a product of primes. For example 60 = 2² × 3 × 5. If a number is written as p^a × q^b × …, the count of factors is (a+1)(b+1)…, so 60 has (2+1)(1+1)(1+1) = 12 factors.

Factors of common numbers

Number	Factors	How many	Prime factorization
12	1, 2, 3, 4, 6, 12	6	2² × 3
24	1, 2, 3, 4, 6, 8, 12, 24	8	2³ × 3
36	1, 2, 3, 4, 6, 9, 12, 18, 36	9	2² × 3²
48	1, 2, 3, 4, 6, 8, 12, 16, 24, 48	10	2⁴ × 3
60	1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60	12	2² × 3 × 5
72	1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72	12	2³ × 3²
100	1, 2, 4, 5, 10, 20, 25, 50, 100	9	2² × 5²
120	1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120	16	2³ × 3 × 5

Need the largest factor two numbers share? Use the GCF and LCM calculator. To test whether a single number is prime, use the prime number checker.

How to use the factor calculator

Type a whole number from 1 to 10,000,000,000,000.
The results update as you type: all factors, factor pairs and prime factorization.
Read whether the number is prime, composite, perfect, abundant or deficient.

Frequently asked questions

What are the factors of 12?

The factors of 12 are 1, 2, 3, 4, 6 and 12. They form the pairs 1 × 12, 2 × 6 and 3 × 4.

What is the difference between factors and multiples?

Factors divide a number exactly and are never larger than it. Multiples are what you get by multiplying the number by 1, 2, 3 and so on, so they are never smaller than it. 3 is a factor of 12; 24 is a multiple of 12.

How do you find the prime factorization of a number?

Divide the number by the smallest prime that goes into it, then repeat with the result until you reach 1. For 60: 60 ÷ 2 = 30, 30 ÷ 2 = 15, 15 ÷ 3 = 5, and 5 is prime, so 60 = 2 × 2 × 3 × 5 = 2² × 3 × 5.

How many factors does a number have?

Write the prime factorization, add 1 to each exponent and multiply the results. 36 = 2² × 3², so it has (2+1)(2+1) = 9 factors: 1, 2, 3, 4, 6, 9, 12, 18 and 36.

Which numbers have an odd number of factors?

Only perfect squares, because one factor pairs with itself. 36 has nine factors and 6 × 6 is its middle pair.

What is a perfect number?

A number equal to the sum of its factors other than itself. 6 is perfect because 1 + 2 + 3 = 6. The next ones are 28, 496 and 8,128.

← All tools