ACT Math : Factors / Multiples
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Example Questions
Example Question #11 : Factors / Multiples
What is the GCF of 36, 64, and 144?
6
36
12
4
2
4
GCF=greatest common factor. First find the factors of each number. So the factors for each number are
36: 1, 36, 2, 18, 3, 12, 4, 9, 6
64: 1, 64, 2, 32, 4, 16
144:1, 144, 2, 72, 3, 48, 4, 36, 6, 24, 8, 18, 9, 16, 12.
1, 2, and 4 are the only factors that are common to 36, 64, and 144. Since 4 is the greatest of these factors, it is the correct answer.
Example Question #1 : How To Find The Greatest Common Factor A1
What is the greatest common factor of 36,108, and 180?
36
18
2
3
5
36
We can find the greatest common factor of a series of numbers by performing the prime factorization of each number. The greatest common factor will be the product of the combinations of prime factors that each number has in common. 36 can be factorized to 22 * 32.108 can be factorized to 22 * 33. 180 can be factorized to 32 * 22 * 5. The greatest common prime factorization is 22 * 32, the product of which is 36. So 36 is the greatest common factor. Remember that 22 * 33 = 22 * 32 * 3.
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 #1651 : Act Math
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
3/9
6/9
5/9
4/9
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.
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