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Factor Calculator

Find all factors, factor pairs, and prime factorizations of a positive integer.

Enter a Positive Integer

How factors are determined

Factors are numbers that divide an integer completely with no remainder. For any number N, the factors always occur in pairs: if A is a factor of N, then B = N / A is also a factor.

Divisibility Search Boundary

To find all divisors of a number efficiently, it is only necessary to check divisibility up to the square root of the number. Any factor above the square root must pair with a factor below the square root. This limit dramatically speeds up calculations for larger integers.

Frequently Asked Questions (FAQ)

What is a factor in math?

A factor is any whole number that divides into another number evenly, meaning it leaves a remainder of zero. For example, the factors of 6 are 1, 2, 3, and 6.

What are factor pairs?

Factor pairs are pairs of two integers that, when multiplied together, equal the original number. For example, the factor pairs of 12 are (1, 12), (2, 6), and (3, 4).

Can factors be negative numbers?

Yes. Every positive factor of a number has a corresponding negative factor. For example, since 2 × 5 = 10, then (-2) × (-5) = 10, meaning -2 and -5 are also factors of 10.

How do you find all the factors of a number?

Divide the number systematically by every integer starting from 1 up to the square root of the number. If there is no remainder, both the divisor and the resulting quotient are factors of that number.

What is a prime factor?

A prime factor is a divisor of a number that is also a prime number (it has no factors other than 1 and itself). For example, the factors of 12 are 1, 2, 3, 4, 6, and 12, but its prime factors are only 2 and 3.

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