All ACT Math Resources
Example Questions
Example Question #21 : Factors / Multiples
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 #1661 : Act Math
If a and b are both factors of 64, which of the following could be a * b?
200
1920
128
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 #21 : Factors / Multiples
Which of the following lists all the factors of 36?
1, 2, 3, 4, 6, 9, 12, 18, 36
1, 36
2, 4, 12, 18, 36
36, 72
2, 3
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 #592 : Arithmetic
What are the factors of the number 12?
2, 6
3, 4
1, 12
2, 3, 6
1, 2, 3, 4, 6, 12
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 #83 : Integers
What is the sum of the greatest common factor (GCF) and the least common multiple (LCM) of , , and ?
: the largest factor that divides evenly into all numbers
: the smallest non-zero number that divides evenly into all numbers. If you are unable to find the GCF, then it is 1.
Prime factorize all numbers:
, because all numbers are relatively prime.
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 , begin by dividing by :
Now, this is a bit trickier for . This happens to be divisible by :
also is divisible by :
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 and that number. So, for , we get:
At this point, things begin to repeat. Thus, the total number of factors is .
Example Question #2 : How To Factor A Number
What is the median value of the factors of ?
There is no median.
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 and that number. So, for , we get:
At this point, the values begin to repeat. This means that there are an even number of factors. At the "middle" of the list, we find and . To find the median of the list, you merely need to take the average of these two numbers: