Factors

Factors refer to numbers that can be multiplied together to reach a specific product. For example, 2 and 3 are factors of 6 because their product is 6. Quadratic factors were discussed above, while this section will focus on whole number/constant factors. These types of factors usually come up on the ACT in the following ways:

Greatest Common Factor

Similar to the Least Common Multiple expressed above, the Greatest Common Factor is the largest factor that is shared between a set of numbers.

So instead of looking for the smallest number that every number in the set factors into. Now, the goal is to find the largest number of the factors into the numbers in the set. Put another way:

• Least Common Multiple looks at the set of numbers as factors
• Greatest Common Factor looks for factors of the set

For example, the Greatest Common Factor of the set: 12, 24, 42 is 6, because it is the last whole number that divides evenly into all numbers of the set.

Prime Factorization

Some Greatest Common Factor questions will ask about the concept of Prime Factorization.

• Prime Factorization means factoring a number using only prime numbers. In other words, figuring out what prime numbers need to be multiplied together to reach a given number.

For example, the prime factorization of 60 would look like this: 5•3•2•2

To get the prime factorization of any number, factor it normally, and then keep factoring until all of the numbers in the sequence are prime. Regardless of which factors you start with, the end product will be the same.

60 = 20 • 3 =  5 • 4 • 3= 5 • 3 • 2 • 2

60 = 15  • 4= 5 • 3 • 4= 5 • 3 • 2 • 2