ACT Math : How to factor a number

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #1 : Other 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?

Possible Answers:
7
15
4
17
13
Correct answer: 7
Explanation:

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 : Other Factors / Multiples

If a and b are both factors of 64, which of the following could be a * b?

Possible Answers:

128

1920

200

34

Correct answer:

128

Explanation:

The factors of 64 are: 1,2,4,8,16,32,64. Therefore, 128 could be the product of 16 and 8.

Example Question #1 : How To Factor A Number

Which of the following is not a factor of 52?

Possible Answers:

13\displaystyle 13

26\displaystyle 26

2\displaystyle 2

4\displaystyle 4

3\displaystyle 3

Correct answer:

3\displaystyle 3

Explanation:

Listing all the factors of 52: 1,2,4,13,26,52.

3 is not one of the factors.

Example Question #2 : How To Factor A Number

Which of the following lists all the factors of 36?

Possible Answers:

2, 3

1, 2, 3, 4, 6, 9, 12, 18, 36

1, 36

2, 4, 12, 18, 36

36, 72

Correct answer:

1, 2, 3, 4, 6, 9, 12, 18, 36

Explanation:

1, 2, 3, 4, 6, 9, 12, 18, 36 are all of the factors of 36. 

Example Question #4 : Other Factors / Multiples

What are the factors of the number 12?

Possible Answers:

1, 12

2, 6

2, 3, 6

3, 4

1, 2, 3, 4, 6, 12

Correct answer:

1, 2, 3, 4, 6, 12

Explanation:

The factors of a number are all the numbers that can be multiplied by an integer to get that number.

Example Question #1 : How To Factor A Number

What is the sum of the greatest common factor (GCF) and the least common multiple (LCM) of \displaystyle 10, \displaystyle 12, and \displaystyle 15?

Possible Answers:

\displaystyle 33

\displaystyle 57

\displaystyle 48

\displaystyle 72

\displaystyle 61

Correct answer:

\displaystyle 61

Explanation:

\displaystyle GCF:  the largest factor that divides evenly into all numbers

\displaystyle LCM:  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:

\displaystyle 10 = 2\cdot 5

\displaystyle 12 = 2\cdot 2\cdot 3

\displaystyle 15 = 3\cdot 5

\displaystyle GCF \displaystyle = 1, because all numbers are relatively prime.

\displaystyle LCM \displaystyle =  \displaystyle 2\cdot 2\cdot 3\cdot 5 = 60

Therefore, \displaystyle GCF + LCM = 1 + 60 = 61.

Example Question #7 : How To Factor A Number

What is the power of the greatest prime factor of \displaystyle 3185000?

Possible Answers:

\displaystyle 3

\displaystyle 2

\displaystyle 1

\displaystyle 5

4

Correct answer:

\displaystyle 1

Explanation:

To get the answer to this question, just carefully prime factor the value \displaystyle 3185000:

First, \displaystyle 3185000= 3185 * 1000

Now, \displaystyle 1000 = 10^3 = 2*2*2*5*5*5 = 2^35^3 

For \displaystyle 3185, begin by dividing by \displaystyle 5:

\displaystyle 3185 = 5 * 637

Now, this is a bit trickier for \displaystyle 637. This happens to be divisible by \displaystyle 7:

\displaystyle 637 = 7 * 91

\displaystyle 91 also is divisible by \displaystyle 7:

\displaystyle 91 = 7 * 13

Thus, your total answer is:

\displaystyle 3185000 = 2^35^47^213^1

Example Question #21 : Factors / Multiples

How many factors are there for the number \displaystyle 42?

Possible Answers:

\displaystyle 7

\displaystyle 4

\displaystyle 3

\displaystyle 8

\displaystyle 5

Correct answer:

\displaystyle 8

Explanation:

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 \displaystyle 1 and that number. So, for \displaystyle 42, we get:

\displaystyle 1 * 42

\displaystyle 2*21

\displaystyle 3*14

\displaystyle 6*7

At this point, things begin to repeat. Thus, the total number of factors is \displaystyle 8.

Example Question #1662 : Act Math

What is the median value of the factors of \displaystyle 60?

Possible Answers:

\displaystyle 8

\displaystyle 6

There is no median.

\displaystyle 10

\displaystyle 8.5

Correct answer:

\displaystyle 8

Explanation:

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 \displaystyle 1 and that number. So, for \displaystyle 60, we get:

\displaystyle 1*60

\displaystyle 2*30

\displaystyle 3*20

\displaystyle 4*15

\displaystyle 5*12

\displaystyle 6*10

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 \displaystyle 6 and \displaystyle 10. To find the median of the list, you merely need to take the average of these two numbers:

\displaystyle \frac{6+10}{2}=\frac{16}{2}=8

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