Find all factors (divisors) of a positive integer, prime factorization, factor pairs, and check if a number is prime or perfect.
| Divisor | Quotient |
|---|---|
| 2 | 180 |
| 2 | 90 |
| 2 | 45 |
| 3 | 15 |
| 3 | 5 |
| 5 | 1 |
| # | Factor A | Factor B | Check |
|---|---|---|---|
| 1 | 1 | 360 | 1 × 360 = 360 |
| 2 | 2 | 180 | 2 × 180 = 360 |
| 3 | 3 | 120 | 3 × 120 = 360 |
| 4 | 4 | 90 | 4 × 90 = 360 |
| 5 | 5 | 72 | 5 × 72 = 360 |
| 6 | 6 | 60 | 6 × 60 = 360 |
| 7 | 8 | 45 | 8 × 45 = 360 |
| 8 | 9 | 40 | 9 × 40 = 360 |
| 9 | 10 | 36 | 10 × 36 = 360 |
| 10 | 12 | 30 | 12 × 30 = 360 |
| 11 | 15 | 24 | 15 × 24 = 360 |
| 12 | 18 | 20 | 18 × 20 = 360 |
Our free factor calculator finds every factor of a number, groups them into factor pairs, breaks the number down into its prime factorization, and identifies whether the number is prime or a perfect number. It's built for students studying number theory, factoring, and divisibility.
A factor of a number n is any integer that divides n evenly with no remainder. This calculator checks every integer up to the square root of n, since factors always come in pairs that multiply to n (if i is a factor, so is n ÷ i).
Prime factorization breaks a number down into the prime numbers that multiply together to produce it, written in exponent form (e.g., 360 = 2³ × 3² × 5). Every whole number greater than 1 has a unique prime factorization, a principle known as the Fundamental Theorem of Arithmetic.
A number is prime if it has exactly two factors (1 and itself). A number is "perfect" if the sum of its factors, excluding itself, equals the number (like 6 = 1 + 2 + 3).
A factor of a number divides into it evenly (factors of 12 include 1, 2, 3, 4, 6, 12). A multiple of a number is what you get by multiplying it by an integer (multiples of 12 include 12, 24, 36). They describe opposite relationships.
Prime factorization is used to find the GCF and LCM of numbers, simplify fractions, solve problems in cryptography, and understand a number's fundamental structure. It's a foundational concept in number theory.
A number is prime if it has no factors other than 1 and itself. You only need to check for factors up to its square root, if none divide evenly, the number is prime.
A perfect number equals the sum of its proper divisors (all factors except itself). The first four perfect numbers are 6, 28, 496, and 8,128, they're rare and become increasingly large as you go further.