EIII Studyhelper 02 Math

1. What is the prime factorization of 9?

3 x 3

3 x 4

1 x 9

The prime factorization of a number involves breaking it down into its prime factors. In the case of 9, the prime factors are both 3. This means that when you multiply 3 by 3, you get 9. Therefore, the prime factorization of 9 is 3 x 3.

Explanation

The prime factorization of a number involves breaking it down into its prime factors. In the case of 9, the prime factors are both 3. This means that when you multiply 3 by 3, you get 9. Therefore, the prime factorization of 9 is 3 x 3.

2. What is the greatest common factor of 6 and 9?

3

6

9

The greatest common factor (GCF) is the largest number that divides evenly into both 6 and 9. In this case, the factors of 6 are 1, 2, 3, and 6, while the factors of 9 are 1, 3, and 9. The largest number that appears in both lists is 3, so it is the GCF of 6 and 9.

Explanation

The greatest common factor (GCF) is the largest number that divides evenly into both 6 and 9. In this case, the factors of 6 are 1, 2, 3, and 6, while the factors of 9 are 1, 3, and 9. The largest number that appears in both lists is 3, so it is the GCF of 6 and 9.

3. Beside 1 and 9, what is the other factor of 9?

The other factor of 9, beside 1 and 9, is 3. Factors are numbers that can be multiplied together to get a given number. In this case, 1 multiplied by 9 equals 9, and 3 multiplied by 3 also equals 9. Therefore, 3 is the other factor of 9.

Explanation

The other factor of 9, beside 1 and 9, is 3. Factors are numbers that can be multiplied together to get a given number. In this case, 1 multiplied by 9 equals 9, and 3 multiplied by 3 also equals 9. Therefore, 3 is the other factor of 9.

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4. What is the gcf of 21 and 35?

3

5

7

The greatest common factor (gcf) is the largest number that divides evenly into both 21 and 35. In this case, the factors of 21 are 1, 3, 7, and 21, while the factors of 35 are 1, 5, 7, and 35. The largest number that appears in both lists is 7, so the gcf of 21 and 35 is 7.

Explanation

The greatest common factor (gcf) is the largest number that divides evenly into both 21 and 35. In this case, the factors of 21 are 1, 3, 7, and 21, while the factors of 35 are 1, 5, 7, and 35. The largest number that appears in both lists is 7, so the gcf of 21 and 35 is 7.

5. Beside 1 and 25, what is the other factor of 25?

The question asks for the other factor of 25 besides 1. A factor of a number is a number that divides evenly into that number. Since 5 is the only other number that divides evenly into 25, it is the correct answer.

Explanation

The question asks for the other factor of 25 besides 1. A factor of a number is a number that divides evenly into that number. Since 5 is the only other number that divides evenly into 25, it is the correct answer.

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6. What is the greatest common factor of 10 and 6?

2

6

16

The greatest common factor (GCF) is the largest number that divides evenly into both given numbers. In this case, the factors of 10 are 1, 2, 5, and 10, while the factors of 6 are 1, 2, 3, and 6. The largest number that appears in both lists is 2, making it the GCF of 10 and 6.

Explanation

The greatest common factor (GCF) is the largest number that divides evenly into both given numbers. In this case, the factors of 10 are 1, 2, 5, and 10, while the factors of 6 are 1, 2, 3, and 6. The largest number that appears in both lists is 2, making it the GCF of 10 and 6.

7. What is the gcf of 22 and 33?

4

13

11

The greatest common factor (GCF) is the largest number that divides both 22 and 33 without leaving a remainder. In this case, the GCF of 22 and 33 is 11 because it is the largest number that can evenly divide both 22 and 33.

Explanation

The greatest common factor (GCF) is the largest number that divides both 22 and 33 without leaving a remainder. In this case, the GCF of 22 and 33 is 11 because it is the largest number that can evenly divide both 22 and 33.

8. What is the prime factorization of 28?

2 x 2 x 7

4 x 7

1 x 28

The prime factorization of a number involves breaking it down into its prime factors. In this case, the number 28 can be expressed as the product of its prime factors, which are 2 and 7. Therefore, the prime factorization of 28 is 2 x 2 x 7.

Explanation

The prime factorization of a number involves breaking it down into its prime factors. In this case, the number 28 can be expressed as the product of its prime factors, which are 2 and 7. Therefore, the prime factorization of 28 is 2 x 2 x 7.

9. What is the greatest common factor of 20 and 12?

4

5

6

The greatest common factor (GCF) is the largest number that divides evenly into both 20 and 12. To find the GCF, we can list the factors of each number and find the largest one they have in common. The factors of 20 are 1, 2, 4, 5, 10, and 20. The factors of 12 are 1, 2, 3, 4, 6, and 12. The largest number that appears in both lists is 4, so the GCF of 20 and 12 is 4.

Explanation

The greatest common factor (GCF) is the largest number that divides evenly into both 20 and 12. To find the GCF, we can list the factors of each number and find the largest one they have in common. The factors of 20 are 1, 2, 4, 5, 10, and 20. The factors of 12 are 1, 2, 3, 4, 6, and 12. The largest number that appears in both lists is 4, so the GCF of 20 and 12 is 4.

10. What is the gcf of 20 and 64?

4

6

16

The greatest common factor (GCF) is the largest number that can evenly divide both given numbers. In this case, the GCF of 20 and 64 is 4. This is because 4 is the largest number that can divide both 20 and 64 without leaving a remainder.

Explanation

The greatest common factor (GCF) is the largest number that can evenly divide both given numbers. In this case, the GCF of 20 and 64 is 4. This is because 4 is the largest number that can divide both 20 and 64 without leaving a remainder.

11. Is 9 the gcf of 18 and 45?

Yes

No

The gcf of 18 and 45 is 9.

Explanation

The gcf of 18 and 45 is 9.

12. Is 7 the gcf of 49 and 70?

Yes

No

The greatest common factor (GCF) is the largest number that divides evenly into two or more numbers. In this case, we need to find the GCF of 49 and 70. To determine if 7 is the GCF, we check if it divides both numbers without any remainder. 7 divides 49 evenly (49 ÷ 7 = 7) and also divides 70 evenly (70 ÷ 7 = 10). Therefore, 7 is the GCF of 49 and 70.

Explanation

The greatest common factor (GCF) is the largest number that divides evenly into two or more numbers. In this case, we need to find the GCF of 49 and 70. To determine if 7 is the GCF, we check if it divides both numbers without any remainder. 7 divides 49 evenly (49 ÷ 7 = 7) and also divides 70 evenly (70 ÷ 7 = 10). Therefore, 7 is the GCF of 49 and 70.

13. Is 4 a prime number?

Yes

No

$ is a composite number. It's factors are 1, 2 and 4.

Explanation

$ is a composite number. It's factors are 1, 2 and 4.

14. What is the greatest common factor of 60 and 80?

10

20

30

The greatest common factor (GCF) is the largest number that divides evenly into both 60 and 80. To find the GCF, we can list the factors of both numbers and find the largest one they have in common. The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60. The factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, and 80. The largest number that appears in both lists is 20, so the GCF of 60 and 80 is 20.

Explanation

The greatest common factor (GCF) is the largest number that divides evenly into both 60 and 80. To find the GCF, we can list the factors of both numbers and find the largest one they have in common. The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60. The factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, and 80. The largest number that appears in both lists is 20, so the GCF of 60 and 80 is 20.

15. Sixteen is a prime number.

True

False

The factors of 16 are more than 2. The factors of 16 are 1, 2, 4, 8 and 16

Explanation

The factors of 16 are more than 2. The factors of 16 are 1, 2, 4, 8 and 16

16. What is the greatest whole number that will divide 45 and 30?

8

15

10

The gcf of 45 and 30 is 15.

Explanation

The gcf of 45 and 30 is 15.

17. What is the prime factorization of 15?

1 x 15

3 x 5

2 x 3 x 5

The prime factorization of 15 is 3 x 5 because 3 and 5 are both prime numbers and when multiplied together, they equal 15.

Explanation

The prime factorization of 15 is 3 x 5 because 3 and 5 are both prime numbers and when multiplied together, they equal 15.

18. What is the prime factorization of 34?

1 x 34

2 x 17

34

The prime factorization of a number involves breaking it down into its prime factors. In this case, the number 34 can be expressed as the product of the prime numbers 2 and 17. Therefore, the prime factorization of 34 is 2 x 17.

Explanation

The prime factorization of a number involves breaking it down into its prime factors. In this case, the number 34 can be expressed as the product of the prime numbers 2 and 17. Therefore, the prime factorization of 34 is 2 x 17.

19. What is the greatest common factor of 12 and 18?

6

12

9

The greatest common factor (GCF) is the largest number that divides evenly into two or more given numbers. In this case, we need to find the GCF of 12 and 18. The factors of 12 are 1, 2, 3, 4, 6, and 12, while the factors of 18 are 1, 2, 3, 6, 9, and 18. The largest number that appears in both lists is 6, so the GCF of 12 and 18 is 6.

Explanation

The greatest common factor (GCF) is the largest number that divides evenly into two or more given numbers. In this case, we need to find the GCF of 12 and 18. The factors of 12 are 1, 2, 3, 4, 6, and 12, while the factors of 18 are 1, 2, 3, 6, 9, and 18. The largest number that appears in both lists is 6, so the GCF of 12 and 18 is 6.

20. Thirteen is a prime number.

True

False

A prime number is a number that is only divisible by 1 and itself. Thirteen is a prime number because it can only be divided by 1 and 13 without any remainder.

Explanation

A prime number is a number that is only divisible by 1 and itself. Thirteen is a prime number because it can only be divided by 1 and 13 without any remainder.

21. What is the prime factorization of 45?

3 x 3 x 5

1 x 45

5 x 9

The prime factorization of a number involves breaking it down into its prime factors. In this case, the number 45 can be expressed as the product of its prime factors, which are 3 and 5. Therefore, the prime factorization of 45 is 3 x 3 x 5.

Explanation

The prime factorization of a number involves breaking it down into its prime factors. In this case, the number 45 can be expressed as the product of its prime factors, which are 3 and 5. Therefore, the prime factorization of 45 is 3 x 3 x 5.

22. Check all the factor pairs of 30.

1 x 30

2 x 16

3 x 10

4 x 8

5 x 6

2 x 15

8 x 6

The correct answer includes the factor pairs of 30, which are 1 x 30, 3 x 10, 5 x 6, and 2 x 15. These pairs are obtained by finding all the possible combinations of two numbers that multiply to give 30.

Explanation

The correct answer includes the factor pairs of 30, which are 1 x 30, 3 x 10, 5 x 6, and 2 x 15. These pairs are obtained by finding all the possible combinations of two numbers that multiply to give 30.

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23. Is 6 the gcf of 18 and 60?

Yes

No

The gcf of 18 and 60 is 6.

Explanation

The gcf of 18 and 60 is 6.

24. Eighteen is NOT a composite number.

True

False

Eighteen is a composite number. The factors of 18 are 1, 2, 3, 6, 9 and 18.

Explanation

Eighteen is a composite number. The factors of 18 are 1, 2, 3, 6, 9 and 18.

25. Is 9 a prime number?

Yes

No

9 is a composite number. Its factors are 1, 3 and 9.

Explanation

9 is a composite number. Its factors are 1, 3 and 9.

26. What is the gcf of 20, 36 and 64?

4

6

8

The greatest common factor (GCF) is the largest number that divides evenly into all of the given numbers. In this case, the GCF of 20, 36, and 64 is 4 because it is the largest number that can divide evenly into all three numbers.

Explanation

The greatest common factor (GCF) is the largest number that divides evenly into all of the given numbers. In this case, the GCF of 20, 36, and 64 is 4 because it is the largest number that can divide evenly into all three numbers.

27. What is the prime factorization of 32?

1 x 32

2 x 2 x 2 x 2 x 2

2 x 2 x 8

The prime factorization of 32 is 2 x 2 x 2 x 2 x 2. This means that 32 can be expressed as the product of prime numbers, where all the prime factors are 2.

Explanation

The prime factorization of 32 is 2 x 2 x 2 x 2 x 2. This means that 32 can be expressed as the product of prime numbers, where all the prime factors are 2.

28. Check all the factors of 18

1

2

3

4

5

6

7

8

9

18

The factors of a number are the numbers that can be multiplied together to get that number. In this case, the factors of 18 are 1, 2, 3, 6, 9, and 18. These numbers can all be multiplied together in different combinations to equal 18.

Explanation

The factors of a number are the numbers that can be multiplied together to get that number. In this case, the factors of 18 are 1, 2, 3, 6, 9, and 18. These numbers can all be multiplied together in different combinations to equal 18.

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29. Check all the factor pairs of 36.

1 x 36

3 x 12

4 x 9

2 x 18

6 x 6

5 x 8

3 x 14

8 x 6

The given answer lists all the factor pairs of 36 correctly. A factor pair is a pair of numbers that, when multiplied together, result in the given number. In this case, the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. The answer correctly lists all the possible combinations of these factors, such as 1 x 36, 3 x 12, 4 x 9, 2 x 18, and 6 x 6.

Explanation

The given answer lists all the factor pairs of 36 correctly. A factor pair is a pair of numbers that, when multiplied together, result in the given number. In this case, the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. The answer correctly lists all the possible combinations of these factors, such as 1 x 36, 3 x 12, 4 x 9, 2 x 18, and 6 x 6.

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30. The greatest divisor of 36 and 12 is 12.

Yes

No

The gcf of 36 and 12 is 12.

Explanation

The gcf of 36 and 12 is 12.

31. What is the gcf of 20, 40 and 60?

10

20

40

The greatest common factor (GCF) is the largest number that divides evenly into all the given numbers. In this case, the GCF of 20, 40, and 60 is 20 because it is the largest number that can divide all three numbers without leaving a remainder.

Explanation

The greatest common factor (GCF) is the largest number that divides evenly into all the given numbers. In this case, the GCF of 20, 40, and 60 is 20 because it is the largest number that can divide all three numbers without leaving a remainder.

32. Check all the factors of 24.

1

2

3

4

5

6

7

8

9

10

11

12

13

14

24

The factors of a number are the numbers that can divide evenly into that number without leaving a remainder. In this case, the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. These numbers can all divide evenly into 24, meaning that when you divide 24 by any of these numbers, you get a whole number without any remainder.

Explanation

The factors of a number are the numbers that can divide evenly into that number without leaving a remainder. In this case, the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. These numbers can all divide evenly into 24, meaning that when you divide 24 by any of these numbers, you get a whole number without any remainder.

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33. Is 4 the gcf of 24 and 32?

Yes

No

The gcf of 24 and 32 is 8.

Explanation

The gcf of 24 and 32 is 8.

34. What is the greatest common factor of 48 and 64?

6

16

8

The greatest common factor (GCF) is the largest number that divides evenly into both 48 and 64. 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 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48. The factors of 64 are 1, 2, 4, 8, 16, 32, and 64. The largest number that appears in both lists is 16, so the GCF of 48 and 64 is 16.

Explanation

The greatest common factor (GCF) is the largest number that divides evenly into both 48 and 64. 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 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48. The factors of 64 are 1, 2, 4, 8, 16, 32, and 64. The largest number that appears in both lists is 16, so the GCF of 48 and 64 is 16.