How to factor a number - ACT Math
Card 0 of 9
Which of the following lists all the factors of 36?
Which of the following lists all the factors of 36?
1, 2, 3, 4, 6, 9, 12, 18, 36 are all of the factors of 36.
1, 2, 3, 4, 6, 9, 12, 18, 36 are all of the factors of 36.
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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?
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
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
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What are the factors of the number 12?
What are the factors of the number 12?
The factors of a number are all the numbers that can be multiplied by an integer to get that number.
The factors of a number are all the numbers that can be multiplied by an integer to get that number.
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If a and b are both factors of 64, which of the following could be a * b?
If a and b are both factors of 64, which of the following could be a * b?
The factors of 64 are: 1,2,4,8,16,32,64. Therefore, 128 could be the product of 16 and 8.
The factors of 64 are: 1,2,4,8,16,32,64. Therefore, 128 could be the product of 16 and 8.
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Which of the following is not a factor of 52?
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.
Listing all the factors of 52: 1,2,4,13,26,52.
3 is not one of the factors.
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What is the sum of the greatest common factor (GCF) and the least common multiple (LCM) of 
, 
, and 
?
What is the sum of the greatest common factor (GCF) and the least common multiple (LCM) of
: 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, 
.
Prime factorize all numbers:
Therefore,
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What is the power of the greatest prime factor of 
?
What is the power of the greatest prime factor of
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:
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:
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How many factors are there for the 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 
.
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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What is the median value of the factors of 
?
What is the median value of the factors of
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:
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, the values begin to repeat. This means that there are an even number of factors. At the "middle" of the list, we find
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