ACT Math - How to factor a number

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?

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

What is the median value of the factors of ?

There is no median.

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 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:

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

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

128

200

1920

Explanation

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

What is the power of the greatest prime factor of ?

Explanation

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:

What are the factors of the number 12?

1, 2, 3, 4, 6, 12

2, 6

3, 4

2, 3, 6

1, 12

Explanation

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

Which of the following lists all the factors of 36?

1, 36

2, 3

36, 72

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

2, 4, 12, 18, 36

Explanation

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

Which of the following is not a factor of 52?

$3$

$2$

$26$

$4$

$13$

Explanation

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

3 is not one of the factors.

How many factors are there for the number ?

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 and that number. So, for , we get: