ACT Math : Factors / Multiples
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Example Questions
Example Question #1 : How To Find Out If A Number Is Prime
How many integers between 2 and 61 are prime numbers, inclusive?
15
18
17
19
16
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 #5 : Prime Numbers
Which of the following sets of numbers contain all prime numbers?
13, 29, 35
13, 25, 31
13, 27, 31
13, 29, 31
13, 27, 33
13, 29, 31
A prime number can only be divided by the number itself and 1.
Example Question #1 : How To Factor A Number
The number 9 is the second smallest integer with 3 factors, 1, 3, and 9. What is the sum of the factors of the smallest integer with only 3 factors?
Here we must do two things. First we must find the smallest integer with 3 factors, then we must add those factors so that we can obtain our answer.
Looking at numbers less than 9 with only 3 factors, the only possibility is the number 4, whose factors are 1, 2, and 4.
The sum of these factors is 1 + 2 + 4 = 7
Example Question #2 : How To Factor A Number
If a and b are both factors of 64, which of the following could be a * b?
128
200
1920
34
128
The factors of 64 are: 1,2,4,8,16,32,64. Therefore, 128 could be the product of 16 and 8.
Example Question #82 : Integers
Which of the following is not a factor of 52?
Listing all the factors of 52: 1,2,4,13,26,52.
3 is not one of the factors.
Example Question #4 : How To Factor A Number
Which of the following lists all the factors of 36?
2, 3
2, 4, 12, 18, 36
1, 36
1, 2, 3, 4, 6, 9, 12, 18, 36
36, 72
1, 2, 3, 4, 6, 9, 12, 18, 36
1, 2, 3, 4, 6, 9, 12, 18, 36 are all of the factors of 36.
Example Question #5 : How To Factor A Number
What are the factors of the number 12?
1, 12
3, 4
2, 6
1, 2, 3, 4, 6, 12
2, 3, 6
1, 2, 3, 4, 6, 12
The factors of a number are all the numbers that can be multiplied by an integer to get that number.
Example Question #6 : How To Factor A Number
What is the sum of the greatest common factor (GCF) and the least common multiple (LCM) of 
Prime factorize all numbers:
Therefore, 
Example Question #7 : How To Factor A Number
What is the power of the greatest prime factor of 
4
To get the answer to this question, just carefully prime factor the value 
First,
Now, 
For 
Now, this is a bit trickier for 
Thus, your total answer is:
Example Question #8 : How To Factor A Number
How many factors are there for the number 
To find the number of factors of a given number, the easiest thing to do is to make a table of the factors, starting with 
At this point, things begin to repeat. Thus, the total number of factors is 
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