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Example Questions
Example Question #82 : Integers
If a and b are both factors of 64, which of the following could be a * b?
34
1920
200
128
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 #24 : Factors / Multiples
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 #1661 : Act Math
Which of the following lists all the factors of 36?
36, 72
1, 2, 3, 4, 6, 9, 12, 18, 36
1, 36
2, 3
2, 4, 12, 18, 36
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 #1 : Other Factors / Multiples
What are the factors of the number 12?
2, 3, 6
3, 4
2, 6
1, 12
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 #1662 : Act Math
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 #3 : 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 #1662 : Act Math
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:
Example Question #1663 : Act Math
If four consecutive odd integers greater than 9 are added together, what is the smallest possible sum of those four integers?
The 4 consecutive of integers greater than 9 (but not including 9) are 11, 13, 15, 17. Added together, we get 56.
Example Question #2 : Sequences
There are two consectutive positive integers and
, and their product is 132.
What is the value of the larger integer?
to find the integers you can guess and check (you know both are larger than 10 because their product is greater than 100) or you can set up a system of equations. if a is the larger number and
.
Therefore:
if you solve that quadratic you get
and b is the smaller number so the bigger number is 12
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