Factor Calculator
Please provide an integer to calculate its factors and prime factors.
What is a factor?
When we multiply numbers, the factors are the whole numbers that are combined to produce another number. For instance, 6 × 5 equals 30; here 6 and 5 act as the factors of 30. Additionally, 1, 2, 3, 10, 15, and 30 are also divisors of 30. In other words, an integer a is a factor of integer b if b divided by a leaves no remainder. Knowing factors helps with fractions and uncovering numeric patterns.
Prime factorization means breaking a number down into the prime numbers that, when multiplied together, recreate the original value. Take 120 as an example: its prime factorization is 2 × 2 × 2 × 3 × 5. Drawing a factor tree can make finding such factorizations easier, as illustrated with 120.
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120
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2 60
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2 30
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2 15
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3 5
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Even with the straightforward case of 120, it becomes clear that determining prime factors can quickly turn into a labor‑intensive task. Currently, no fast algorithm is known for factoring very large integers, so many online calculators—including the one on this page—are limited to modest sizes. Factoring the 232‑digit RSA‑768 required a coordinated effort by several researchers, employing hundreds of machines over two years.
Although no efficient algorithm has been found, it also has yet to be proven that no such algorithm exists, leaving room for anyone interested in having their name in a mathematical algorithm to formulate one (or prove in some self-named theorem that one doesn't exist)!