Sum of Factors Calculator

What Are Factors?

A factor is an integer that divides another number exactly, without leaving a remainder. In other words, if integer \( a \) divides integer \( b \) evenly, then \( a \) is a factor of \( b \). Factors always come in pairs: a smaller factor and a larger factor that, when multiplied together, result in the original number.

For example, the factors of 12 are 1, 2, 3, 4, 6, and 12. These factors can be paired as follows:

Thus, the factors of 12 are: \( (1, 12), (2, 6), (3, 4) \).

Interesting Facts About Factors

• 1 is a factor of every number: Regardless of the size of the number, 1 is always a factor of it.
• A number is also a factor of itself: This is because any number divided by itself equals 1, with no remainder.
• Prime numbers have only two factors: The factors of the prime number are 1 and the number itself. For example, 7 is prime because its only factors are 1 and 7.
• Composite numbers have more than two factors: A composite number has at least one factor other than 1 and itself. For example, 6 is a composite number because it has factors 1, 2, 3, and 6.

How to Calculate the Sum of All Factors of a Number?

To calculate the sum of all factors of a number, follow these two steps:

1. Find all factors: To find all factors of a number, start by checking divisibility for each number from 1 up to the square root of the number. If a number divides evenly, both the divisor and the quotient are factors of the number.
2. Add the factors together: Once all the factors are found, simply add them up to get the total sum of factors.

Examples

Example 1: Calculate the sum of all factors of 12.

Example 2: Calculate the sum of all factors of 36.

Example 3: Calculate the sum of all factors of 100.