Your ACT Math Test will almost certainly feature questions on factors, multiples, and divisors. Out of 60 questions, you can expect these concepts to play a role in at least 2 or 3 questions. This is everything you’ll need to know to get those questions correct on Test Day!
Test your ACT math skills with this ACT math practice question!
Factors
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?
What is the GCF of 36 and 108?
The answer is 36, because 36 is a factor of itself, and 108 is a multiple of 36.
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.
Multiples
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.
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.
Divisibility
Here are the Rules of Divisibility to memorize for the ACT!
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.
For more practice with these rules, click on Create Game in the ACT lobby and create a custom game using these skill tags at the difficulty level of your choice! You can also message any of the Grockit ACT tutors to set up a private tutoring session for more help. Find out more by clicking the Tutoring tab in the Grockit lobby.