ACT Math : Arithmetic
Study concepts, example questions & explanations for ACT Math
All ACT Math Resources
Example Questions
Example Question #71 : Integers
What is the greatest common factor of 56 and 68?
8
7
4
14
4
The factors are as follows:
56: 1,2,4,7,8,14,28,56
68, 1,2,4,17,34,68
The greatest factor that both numbers are divisible by is 4.
Example Question #1 : Greatest Common Factor
What is the greatest common factor of 72 and 84?
18
6
12
10
12
Factors are numbers that can divide evenly into larger numbers. The factors of 72 are 36, 24, 18, 12, 9, 8, 6, 4, 3, and 2. The factors of 84 are 42, 28, 21, 14, 12, 7, 6, 4, 3, and 2. Thefore, the greatest common factor is 12.
Example Question #7 : Greatest Common Factor
What is the greatest common factor (GCF) of 48, 156, and 420?
2
4
12
6
24
12
All three numbers are divisible by 2, 4, 6, and 12, but only 48 is divislbe by 24. Therefore, the greatest common factor of these three numbers is 12.
Example Question #8 : Greatest Common Factor
What is the greatest common factor of 
The greatest common factor is the largest factor that goes into both numbers. Begin by factoring each number:
The common facors are, 
Example Question #3 : Greatest Common Factor
What is the greatest common factor of 
There are two approaches to this question. You can either list all of the factors for each of the numbers given in the question and see which one is the greatest that the three have in common. The other approach is to check each of the three numbers in the question by the answer choices and see which is the greatest factor of all three numbers.
In this case:
Note that 
Example Question #1 : Prime Numbers
What is the probability of selecting a prime number out of the following set?
{2, 6, 9, 17, 21, 47, 63, 71, 81}
9/4
5/9
4/9
6/9
3/9
4/9
Probability is determined by dividing favorable outcomes, by possible outcomes. As there are 9 numbers in the given set, the number of possible outcomes is 9. In the given set, only 2, 17, 47 and 71 are prime numbers (divisible only by 1 and itself). Thus, there are 4 favorable outcomes, yielding a probability of 4/9.
Example Question #2 : Prime Numbers
How many prime numbers between 20 and 40 are divisible by 9?
2
9
1
0
0
Prime numbers are by definition only divisible by themselves and 1.
Example Question #2 : How To Find Out If A Number Is Prime
How many prime numbers are between 40 and 60?
9
5
8
7
6
5
A prime number is a number that is only divisible by 1 and the number itself (examples include 3, 11, 19). The prime numbers between 40 and 60 are 41, 43, 47, 53, and 59.
Example Question #3 : How To Find Out If A Number Is Prime
How many integers between 2 and 61 are prime numbers, inclusive?
17
18
16
19
15
18
The key word is “inclusive.” The answer is 18 prime numbers. If you answered 16, you did not include 2 and 61 as prime numbers. If you answered 17, you only included one of the outer limits in the range. If you answered 15, you did not include the outer limits, 2 and 61, as prime numbers and miscounted. There are 18 prime numbers between 2 and 61 when you include the range’s limits.
Example Question #4 : How To Find Out If A Number Is Prime
Which of the following sets of numbers contain all prime numbers?
13, 27, 33
13, 29, 31
13, 29, 35
13, 25, 31
13, 27, 31
13, 29, 31
A prime number can only be divided by the number itself and 1.
Certified Tutor
All ACT Math Resources
