Other Factors / Multiples

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Questions 1 - 10
1

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?

4

7

13

15

17

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

2

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?

4

7

13

15

17

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

3

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:

4

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:

5

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

128

200

1920

34

Explanation

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

6

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

128

200

1920

34

Explanation

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

7

What is the power of the greatest prime factor of ?

4

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:

8

What is the power of the greatest prime factor of ?

4

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:

9

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.

10

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.

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