## ACT Math Basics

Learning the basics of number properties is crucial for success on the ACT Math Test. Here, you’ll learn some basic terminology to help you on the test.

A **factor**, or divisor, of a number is a positive integer that evenly divides into that number. For example, 4 is a factor of 12 because 12/4 is an integer, 3. All integers have 1 and themselves as factors. For example there are six factors for the number 12: 1, 2, 3, 4, 6, 12.

The GCF, or **greatest common factor**, is the biggest factor that two numbers have in common. Think of GCF questions as: what is the biggest number that divides evenly into both?

A **prime number** is a special kind of integer that has exactly two factors: itself and 1.

Remember that 1 is NOT prime, because it only has one factor, itself. 2 is a special number because it is the smallest prime number and the only even prime number. The first few prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.

A **multiple** is a number that is evenly divisible by another integer. For example, 6 is a multiple of 3. 10 Is a multiple of 5. The multiple is always *larger* than the other integer. The other integer would be considered a factor of the multiple. Every number is a multiple of itself.

For example, for the number 12, possible multiples are 12, 24, 36, 48, 60, etc. The LCM, or **lowest common multiple**, is the smallest number for which both given numbers are factors.

## Practice Question

*What is the LCM of 12 and 9?*

9 = 3 x 3, and 12 = 3 x 4, so the LCM must be 3 x 3 x 4 = 36. By saying that the LCM of 12 and 9 is 36, you are saying that 36 is the SMALLEST number that both 12 and 9 will divide into evenly. Notice how the LCM is not necessarily just the product of the two integers.

## The ACT Math Rules of Divisibility

In addition to factors and multiples, it helps to know some basic divisibility rules – a great shortcut on certain long division problems!

- A number is divisible by 2 if it’s an even number.
- A number is divisible by 3 if the sum of the digits is divisible by 3.
- A number is divisible by 4 if the last two digits are divisible by 4.
- A number is divisible by 5 if the last digit is either 0 or 5.
- A number is divisible by 6 if it’s divisible by BOTH 2 and 3.
- A number is divisible by 9 if the sum of the digits is divisible by 9.

That’s all for this lesson! Brush up on your math basics, then tackle more challenging concepts, like matrices on the ACT. 🙂