Chapter 2 Quiz (2-1 & 2-2)

1) Do you know how to draw a factor tree? There will be one on the quiz.

Yes

No

The question asks whether the person knows how to draw a factor tree and states that there will be one on the quiz. The answer "Yes" indicates that the person does know how to draw a factor tree.

Explanation

The question asks whether the person knows how to draw a factor tree and states that there will be one on the quiz. The answer "Yes" indicates that the person does know how to draw a factor tree.

2) Simplify

9

3

27

6

The given numbers 9, 3, 27, and 6 are all multiples of 3. However, only 27 is not divisible by 9. Therefore, the number 27 is the only one that cannot be simplified further by dividing it by 9, making it the correct answer.

Explanation

The given numbers 9, 3, 27, and 6 are all multiples of 3. However, only 27 is not divisible by 9. Therefore, the number 27 is the only one that cannot be simplified further by dividing it by 9, making it the correct answer.

3) Find the factors of 32.

1, 2, 4, 5, 10, 20

1, 2, 4, 8, 16, 32

32, 64, 96

1, 2, 6, 32

The factors of a number are the numbers that can be multiplied together to get that number. In this case, the factors of 32 are 1, 2, 4, 8, 16, and 32. These numbers can be multiplied in different combinations to equal 32. For example, 2 multiplied by 16 equals 32, or 4 multiplied by 8 equals 32. Therefore, the given answer of 1, 2, 4, 8, 16, 32 is correct.

Explanation

The factors of a number are the numbers that can be multiplied together to get that number. In this case, the factors of 32 are 1, 2, 4, 8, 16, and 32. These numbers can be multiplied in different combinations to equal 32. For example, 2 multiplied by 16 equals 32, or 4 multiplied by 8 equals 32. Therefore, the given answer of 1, 2, 4, 8, 16, 32 is correct.

4) Which of the following numbers is prime?

18

9

68

13

A prime number is a number that is only divisible by 1 and itself. Among the given numbers, 13 is the only one that meets this criteria. 18 is divisible by 1, 2, 3, 6, 9, and 18. 9 is divisible by 1, 3, and 9. 68 is divisible by 1, 2, 4, 17, 34, and 68. Therefore, the only prime number among the options is 13.

Explanation

A prime number is a number that is only divisible by 1 and itself. Among the given numbers, 13 is the only one that meets this criteria. 18 is divisible by 1, 2, 3, 6, 9, and 18. 9 is divisible by 1, 3, and 9. 68 is divisible by 1, 2, 4, 17, 34, and 68. Therefore, the only prime number among the options is 13.

5) Write 6 x 6 x 6 x 6 x 6 as an exponent.

7776

To write 6 x 6 x 6 x 6 x 6 as an exponent, we need to determine the number of times 6 is multiplied by itself. In this case, 6 is multiplied by itself 5 times. Therefore, 6 x 6 x 6 x 6 x 6 can be written as 6^5, which equals 7776.

Explanation

To write 6 x 6 x 6 x 6 x 6 as an exponent, we need to determine the number of times 6 is multiplied by itself. In this case, 6 is multiplied by itself 5 times. Therefore, 6 x 6 x 6 x 6 x 6 can be written as 6^5, which equals 7776.

6) Find the greatest common factor (GCF) of 12 & 15.

8

2

4

3

The greatest common factor (GCF) is the largest number that divides evenly into both 12 and 15. To find the GCF, we can list the factors of both numbers and find the largest number that appears in both lists. The factors of 12 are 1, 2, 3, 4, 6, and 12. The factors of 15 are 1, 3, 5, and 15. The largest number that appears in both lists is 3, so the GCF of 12 and 15 is 3.

Explanation

The greatest common factor (GCF) is the largest number that divides evenly into both 12 and 15. To find the GCF, we can list the factors of both numbers and find the largest number that appears in both lists. The factors of 12 are 1, 2, 3, 4, 6, and 12. The factors of 15 are 1, 3, 5, and 15. The largest number that appears in both lists is 3, so the GCF of 12 and 15 is 3.

7) Write the prime factorization for 60.

4 x 15

2 x 30

2 x 2 x 3 x 5

2 x 5 x 3

Remember to use a factor tree.

Explanation

Remember to use a factor tree.

8) Simplify

256

-256

16

8

Remember to watch your signs
-4 x -4 x -4 x -4
16 x -4 x -4
-64 x -4
256

Explanation

Remember to watch your signs
-4 x -4 x -4 x -4
16 x -4 x -4
-64 x -4
256

9) Simplify

200

88

48

52

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Explanation

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10) Simplify

3

6

1

7

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Explanation

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11) Find the Least Common Multiple (LCM) of 9 and 12.

46

4

3

36

Make sure you don't mix up LCM with GCF.

Multiples of 9: 9, 18, 27, 36, 45...

Multiples of 12: 12, 24, 36, 48...

Least common multiple = 36

Explanation

Make sure you don't mix up LCM with GCF.

Multiples of 9: 9, 18, 27, 36, 45...

Multiples of 12: 12, 24, 36, 48...

Least common multiple = 36