# ACT Number Properties Basics: Factors, Multiples, and Divisibility

## 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. 🙂

## Author

• Magoosh is a company of passionate educators, located in Berkeley, CA. We are here to provide you with everything you need to prep for the ACT, SAT, GRE, GMAT, and TOEFL! Be sure to follow us on Twitter @Magoosh.