What Are the Factors of 45?

The factors of 45 are 1, 3, 9, 15 and 45. A factor is a number or algebraic expression that divides into another number or expression evenly with no remainder.

A positive integer greater than 1 that has only two factors is considered a prime number. Numbers that have more than two factors are considered composite numbers. Factors that are prime numbers are called prime factors. A number can also be expressed in terms of its prime factors, with few exceptions. For example, the number 60 can be expressed as the product of 2, 2, 3 and 5. Methods of factoring large whole numbers is a key part of cryptology, and Internet data security relies on them.

Mathematicians from Pythagoras' School between 500 and 300 B.C. were interested in mystical and numerological properties of numbers. A number was considered a perfect number if its factors, also called divisors, added up to the number itself. For example, the factors of 6 are 1, 2 and 3. Added together, these factors equal 6. Another number that is considered perfect is 28. Amicable numbers are pairs in which the factors of one number add up to the other number, such as 220 and 284.