Factors / Multiples

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ACT Math › Factors / Multiples

Questions 1 - 10
1

A sliced cake can be equally split among 4, 5, or 6 people, with each person receiving the same number of slices. Which of the following answers represents a possible number of slices that the cake could have?

24

30

56

116

120

Explanation

If you divide the answer choices by 4, 5, and 6, 120 is the only choice that divides evenly by all three numbers.

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 probability of selecting a prime number out of the following set?

{2, 6, 9, 17, 21, 47, 63, 71, 81}

3/9

4/9

5/9

6/9

9/4

Explanation

Probability is determined by dividing favorable outcomes, by possible outcomes. As there are 9 numbers in the given set, the number of possible outcomes is 9. In the given set, only 2, 17, 47 and 71 are prime numbers (divisible only by 1 and itself). Thus, there are 4 favorable outcomes, yielding a probability of 4/9.

4

A sliced cake can be equally split among 4, 5, or 6 people, with each person receiving the same number of slices. Which of the following answers represents a possible number of slices that the cake could have?

24

30

56

116

120

Explanation

If you divide the answer choices by 4, 5, and 6, 120 is the only choice that divides evenly by all three numbers.

5

What is the probability of selecting a prime number out of the following set?

{2, 6, 9, 17, 21, 47, 63, 71, 81}

3/9

4/9

5/9

6/9

9/4

Explanation

Probability is determined by dividing favorable outcomes, by possible outcomes. As there are 9 numbers in the given set, the number of possible outcomes is 9. In the given set, only 2, 17, 47 and 71 are prime numbers (divisible only by 1 and itself). Thus, there are 4 favorable outcomes, yielding a probability of 4/9.

6

A sliced cake can be equally split among 4, 5, or 6 people, with each person receiving the same number of slices. Which of the following answers represents a possible number of slices that the cake could have?

24

30

56

116

120

Explanation

If you divide the answer choices by 4, 5, and 6, 120 is the only choice that divides evenly by all three numbers.

7

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

8

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

9

What is the probability of selecting a prime number out of the following set?

{2, 6, 9, 17, 21, 47, 63, 71, 81}

3/9

4/9

5/9

6/9

9/4

Explanation

Probability is determined by dividing favorable outcomes, by possible outcomes. As there are 9 numbers in the given set, the number of possible outcomes is 9. In the given set, only 2, 17, 47 and 71 are prime numbers (divisible only by 1 and itself). Thus, there are 4 favorable outcomes, yielding a probability of 4/9.

10

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:

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