Factor Calculator
List every factor and factor pair of a number, and determine if it's prime.
Inputs
Number of Factors
9
Factors
1, 2, 3, 4, 6, 9, 12, 18, 36
Factor Pairs
1 × 36; 2 × 18; 3 × 12; 4 × 9; 6 × 6
Is Prime?
No — composite (9 factors)
Step by step
Number
= 36
Factors (9)
= 1, 2, 3, 4, 6, 9, 12, 18, 36
Factor pairs
= 1 × 36; 2 × 18; 3 × 12; 4 × 9; 6 × 6
Prime?
= No
How it works
A factor (or divisor) of an integer n is a number that divides n exactly, leaving no remainder. Every positive integer has at least two factors: 1 and itself. A prime number has exactly those two — no others. The factor pairs of n are all (a, b) with a ≤ b and a × b = n. This calculator finds factors by trial division from 1 to √n, which is efficient for numbers up to ~10⁹.
Formulas
Factor condition
d divides n if and only if n mod d = 0
Factor count bound
Factors come in pairs (d, n/d), so total factors ≤ 2√n
Frequently Asked Questions
What makes a number prime?
A prime number has exactly two distinct factors: 1 and itself. Examples: 2, 3, 5, 7, 11, 13. Note that 1 is not prime (it has only one factor), and 2 is the only even prime.
What is the difference between factors and multiples?
Factors divide evenly into n. Multiples are n multiplied by positive integers. The factors of 12 are 1, 2, 3, 4, 6, 12. The multiples of 12 are 12, 24, 36, 48, …
How many factors does 36 have?
36 = 2² × 3². Using the formula for the number of factors: (2+1)(2+1) = 9. The factors are 1, 2, 3, 4, 6, 9, 12, 18, 36.