Factors Calculator

Definitions of Factors

Factors

Factors are all integers that divide a given number without leaving a remainder. Factors can be positive or negative, but in most cases, we consider only positive factors. Example: The factors of 6 are 1, 2, 3, and 6.

Prime Factors

Prime factors are factors that are prime numbers, meaning they can only be divided evenly by 1 and themselves. Example: The prime factors of 6 are 2 and 3.

Proper Factors

Proper factors are all the factors of a number excluding the number itself. Example: The proper factors of 6 are 1, 2, and 3.

How to Calculate Factors

1. Find All Factors: Start at 1 and check each integer to see if it divides the input number evenly. If it does, include it in the list of factors.
2. Identify Prime Factors: Filter the factors to include only the prime numbers.
3. Determine Proper Factors: Remove the number itself from the list of factors to find the proper factors.

Examples

Example 1: Factors, Prime Factors, and Proper Factors of 28

Example 2: Factors, Prime Factors, and Proper Factors of 72

Example 3: Factors, Prime Factors, and Proper Factors of 100

Example 4: Factors, Prime Factors, and Proper Factors of 1