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Factor Calculator

Find all factors, factor pairs, and the prime factorization of a positive integer, with a factor tree.

ExampleSample values — edit any field to see your result.

Enter a positive integer up to 10,000,000,000,000.

Results update as you type.

Result

Composite

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

Estimated result

Factors
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
Factor pairs
(1, 120) (2, 60) (3, 40) (4, 30) (5, 24) (6, 20) (8, 15) (10, 12)
Prime factorization
120 = 2 × 2 × 2 × 3 × 5

Factor tree

Factor tree
120
| \
60 2
| \
30 2
| \
15 2
| \
5 3
Result1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

Enter a positive integer to list its factors and factor pairs, see the prime factorization, and walk a factor tree. For a prime, the result simply says so and shows the pair (1, n).

Formula

An integer a is a factor of n when n ÷ a has remainder 0. The positive factors come in pairs (a, n/a) found by testing a = 1, 2, … up to √n.

Prime factorization. Divide out the smallest prime repeatedly:

120 = 2 × 2 × 2 × 3 × 5

Factor tree (same splits, quotient on the left, prime on the right):

120
| \
60    2
| \
30    2
| \
15    2
| \
5     3

1 is neither prime nor composite; its only pair is (1, 1). A prime has exactly two positive factors, 1 and itself.

Simplifying a fraction a/b uses GCF(a, b), not the full factor list. Open the GCF calculator when you want the greatest common factor of several numbers, or the LCM calculator for the least common multiple.

Examples

Default 120

Factors are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120. Pairs run (1, 120) through (10, 12). Prime factorization is 2 × 2 × 2 × 3 × 5.

Page example 20

Factors 1, 2, 4, 5, 10, 20, pairs (1, 20) (2, 10) (4, 5), and 20 = 2 × 2 × 5.

Prime 7

7 is a prime number. Its only factor pair is (1, 7).

Frequently asked questions

What is a factor?
A factor of an integer n is an integer that divides n with no remainder. For 30, the positive factors are 1, 2, 3, 5, 6, 10, 15, and 30, because each of those multiplies with another integer to make 30 (for example 6 × 5 = 30).
What is prime factorization?
Prime factorization writes a number as a product of primes. 120 is 2 × 2 × 2 × 3 × 5. Every integer greater than 1 has a unique prime factorization (the fundamental theorem of arithmetic), aside from the order of the primes.
How do you build a factor tree?
Split the number into a prime factor and the remaining quotient, then repeat on the quotient until both sides are prime. For 120 the tree peels off 2, 2, 2, then 3, leaving 5: 120 → 60 × 2 → 30 × 2 → 15 × 2 → 5 × 3.
What is the difference between factors and the GCF?
This calculator lists every factor of one integer. The GCF (greatest common factor) calculator finds the largest factor shared by two or more integers. Use LCM when you want the smallest shared multiple instead.
How large a number can I enter?
Positive integers up to 10,000,000,000,000 (10 trillion). Zero, negatives, and non-whole numbers are rejected. There is no known fast algorithm for prime-factorizing arbitrarily large integers, which is why the tool caps the input.

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