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Factor Pairs Calculator

Enter a positive whole number to list all factors and every factor pair from (1, n) to the square-root pair. The result also shows divisor count, divisor sum, perfect-square status, and whether n is prime or composite.

The calculation runs in your browser. A shared result URL contains the number you calculated, so anyone with that URL can see it.

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Input

Use one positive integer from 1 to 9007199254740991. A leading + and leading zeroes are accepted; do not use decimal points, separators, or spaces inside the number.

Result

All positive factors

Factor pairs
# Left factor Right factor Check

How to use this factor pair finder

  1. Enter one positive whole number, such as 36 or 720.
  2. Press List factor pairs to generate the full factor list and pair table.
  3. Use the classification and perfect-square check to decide whether the number is prime, composite, or 1.

Use Prime factorization with steps when you need prime powers, a factor tree, or trial division steps. Use GCD & LCM when you are comparing two or more integers.

Example: factor pairs of 36

For n = 36, the positive factors are 1, 2, 3, 4, 6, 9, 12, 18, and 36. The factor pairs are (1, 36), (2, 18), (3, 12), (4, 9), and (6, 6). The middle pair appears once because 36 is a perfect square.

FAQ

How are factor pairs listed?

Each pair appears once with the smaller positive factor first, and that smaller factor is no greater than √n. For a perfect square, the equal middle pair such as (6, 6) for 36 appears once.

What happens for 1 and prime numbers?

For 1, the only factor pair is (1, 1), and 1 is neither prime nor composite. For a prime number, the only factor pair is (1, n).

What input range does this calculator support?

Enter one positive whole number from 1 through 9007199254740991. Some numbers in this range can reach the calculation limit; in that case, the calculator reports that no complete result was obtained instead of showing an incomplete list.

How is this different from prime factorization?

This page focuses on the full factor list and ordered factor pairs. Use the prime factorization calculator when you need prime powers, trial division steps, or a factor tree.

Does this factor algebraic expressions?

No. This calculator handles one positive integer. It does not factor polynomials or symbolic expressions.