Factor Calculator

Enter any positive integer to find all its factors in pairs, its prime factorization, the total number of factors, and whether it is perfect, abundant, or deficient.

Enter a positive integer (up to 1,000,000).

Number

Classifications Explained

Perfect:Sum of proper divisors equals the number (e.g. 6 = 1+2+3).

Abundant:Sum of proper divisors exceeds the number (e.g. 12: 1+2+3+4+6 = 16 > 12).

Deficient:Sum of proper divisors is less than the number (e.g. 8: 1+2+4 = 7 < 8).

Frequently Asked Questions

What is a factor?

A factor (or divisor) of an integer n is any integer that divides n without a remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.

What is prime factorization?

Prime factorization expresses a number as a product of prime numbers. Every integer greater than 1 has a unique prime factorization. For example, 360 = 2³ × 3² × 5.

How many factors does a number have?

If n = p₁^a₁ × p₂^a₂ × … × pₖ^aₖ, then the number of factors is (a₁+1)(a₂+1)…(aₖ+1). For 360 = 2³ × 3² × 5¹, that is (3+1)(2+1)(1+1) = 24 factors.

What is a perfect number?

A perfect number equals the sum of its proper divisors. The first few perfect numbers are 6, 28, 496, and 8128. Only 51 perfect numbers are known, and all known ones are even.

What is the difference between a factor and a multiple?

A factor divides evenly into a number. A multiple is the result of multiplying a number by an integer. For 4: factors are 1, 2, 4; multiples are 4, 8, 12, 16…