### All ACT Math Resources

## Example Questions

### Example Question #81 : Integers

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:**

**Correct answer:**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

### Example Question #1 : How To Factor A Number

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

**Possible Answers:**

200

128

34

1920

**Correct answer:**

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 #1 : How To Factor A Number

Which of the following is not a factor of 52?

**Possible Answers:**

**Correct answer:**

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

3 is not one of the factors.

### Example Question #1 : Other Factors / Multiples

Which of the following lists all the factors of 36?

**Possible Answers:**

2, 3

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

36, 72

2, 4, 12, 18, 36

1, 36

**Correct answer:**

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 #2 : Other Factors / Multiples

What are the factors of the number 12?

**Possible Answers:**

2, 6

3, 4

2, 3, 6

1, 12

1, 2, 3, 4, 6, 12

**Correct answer:**

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 #1 : How To Factor A Number

What is the sum of the greatest common factor (GCF) and the least common multiple (LCM) of , , and ?

**Possible Answers:**

**Correct answer:**

: 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 #1 : Other Factors / Multiples

What is the power of the greatest prime factor of ?

**Possible Answers:**

4

**Correct answer:**

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 #1 : Other Factors / Multiples

How many factors are there for the number ?

**Possible Answers:**

**Correct answer:**

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 #1 : Other Factors / Multiples

What is the median value of the factors of ?

**Possible Answers:**

There is no median.

**Correct answer:**

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:

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