Factors And Multiples Trivia Quiz Questions And Answers

1. Which number is a multiple of 6?

14

20

32

42

A multiple of 6 is any number that can be obtained by multiplying 6 by an integer. 42 is divisible by 6 (42 / 6 = 7), making it a multiple of 6. The other numbers are not divisible by 6.

Explanation

A multiple of 6 is any number that can be obtained by multiplying 6 by an integer. 42 is divisible by 6 (42 / 6 = 7), making it a multiple of 6. The other numbers are not divisible by 6.

2. How many multiples does 10 have?

4

9

100

An infinity

The number 10 is a multiple of itself, so it can be multiplied by any positive integer to get another multiple of 10. Since there are infinitely many positive integers, there are infinitely many multiples of 10. Therefore, the correct answer is "an infinity".

Explanation

The number 10 is a multiple of itself, so it can be multiplied by any positive integer to get another multiple of 10. Since there are infinitely many positive integers, there are infinitely many multiples of 10. Therefore, the correct answer is "an infinity".

3. What is the greatest common factor of 10 and 45?

10

15

5

8

The greatest common factor (GCF) of two numbers is the largest number that divides both of them without leaving a remainder. In this case, the factors of 10 are 1, 2, 5, and 10, while the factors of 45 are 1, 3, 5, 9, 15, and 45. The largest number that appears in both lists is 5, so the GCF of 10 and 45 is 5.

Explanation

The greatest common factor (GCF) of two numbers is the largest number that divides both of them without leaving a remainder. In this case, the factors of 10 are 1, 2, 5, and 10, while the factors of 45 are 1, 3, 5, 9, 15, and 45. The largest number that appears in both lists is 5, so the GCF of 10 and 45 is 5.

4. Which is the greatest common factor of 45 and 60?

5

15

30

45

The greatest common factor (GCF) of two numbers is the largest number that divides both of them without leaving a remainder. In this case, we need to find the GCF of 45 and 60. To do this, we can list the factors of both numbers and find the largest one they have in common. The factors of 45 are 1, 3, 5, 9, 15, 45 and the factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. The largest factor they have in common is 15, therefore, 15 is the greatest common factor of 45 and 60.

Explanation

The greatest common factor (GCF) of two numbers is the largest number that divides both of them without leaving a remainder. In this case, we need to find the GCF of 45 and 60. To do this, we can list the factors of both numbers and find the largest one they have in common. The factors of 45 are 1, 3, 5, 9, 15, 45 and the factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. The largest factor they have in common is 15, therefore, 15 is the greatest common factor of 45 and 60.

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

2

4

6

9

The greatest common factor (GCF) is the largest number that divides evenly into both 12 and 18. To find the GCF, we can list the factors of each number 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 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 both 12 and 18. To find the GCF, we can list the factors of each number 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 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.

6. A number is a multiple of 6 if ________________________

The last digit is 6

Its last two digits form a number divisible by 6

The sum of all of its digits is divisible by 6

The sum of all its digits is divisible by 3 and the last digit is even

A number is a multiple of 6 if the sum of all its digits is divisible by 3 and the last digit is even. This is because 6 is divisible by both 2 and 3. Therefore, for a number to be a multiple of 6, it must be divisible by 2 (which means the last digit must be even) and also divisible by 3 (which means the sum of all its digits must be divisible by 3).

Explanation

A number is a multiple of 6 if the sum of all its digits is divisible by 3 and the last digit is even. This is because 6 is divisible by both 2 and 3. Therefore, for a number to be a multiple of 6, it must be divisible by 2 (which means the last digit must be even) and also divisible by 3 (which means the sum of all its digits must be divisible by 3).

7. Which pair of numbers has 60 as their least common multiple?

12 and 30

30 and 45

40 and 60

10 and 6

The numbers 12 and 30 have 60 as their least common multiple. The least common multiple (LCM) of two numbers is the smallest multiple that both numbers have in common. To find the LCM, we can list the multiples of each number and find the smallest common multiple. The multiples of 12 are 12, 24, 36, 48, 60, ... and the multiples of 30 are 30, 60, 90, 120, ... The smallest multiple that both numbers have in common is 60, so 12 and 30 have 60 as their LCM.

Explanation

The numbers 12 and 30 have 60 as their least common multiple. The least common multiple (LCM) of two numbers is the smallest multiple that both numbers have in common. To find the LCM, we can list the multiples of each number and find the smallest common multiple. The multiples of 12 are 12, 24, 36, 48, 60, ... and the multiples of 30 are 30, 60, 90, 120, ... The smallest multiple that both numbers have in common is 60, so 12 and 30 have 60 as their LCM.

8. Which number is a factor of 111?

3

9

11

21

A factor of a number is a number that divides evenly into that number without leaving a remainder. In this case, 3 is a factor of 111 because 111 divided by 3 equals 37, with no remainder. Therefore, 3 is a factor of 111.

Explanation

A factor of a number is a number that divides evenly into that number without leaving a remainder. In this case, 3 is a factor of 111 because 111 divided by 3 equals 37, with no remainder. Therefore, 3 is a factor of 111.

9. Which two numbers are relatively prime?

9 and 16

18 and 27

21 and 56

30 and 45

Two numbers are relatively prime if their greatest common divisor (GCD) is 1, meaning they have no common factors other than 1. The numbers 9 and 16 are relatively prime because the only common factor between them is 1. The other pairs (18 and 27, 21 and 56, 30 and 45) share common factors greater than 1, so they are not relatively prime.

Explanation

Two numbers are relatively prime if their greatest common divisor (GCD) is 1, meaning they have no common factors other than 1. The numbers 9 and 16 are relatively prime because the only common factor between them is 1. The other pairs (18 and 27, 21 and 56, 30 and 45) share common factors greater than 1, so they are not relatively prime.

10. Which of the following are factors of 1710?

2,4,5,10

2,5,7,10

2,5,10

2,3,5,8,10

Factors of a number are integers that divide the number exactly without leaving a remainder. For 1710, the factors include 2, 5, and 10 because 1710 can be divided by these numbers with no remainder (e.g., 1710 ÷ 2 = 855). However, numbers like 4, 7, and 8 are not factors of 1710 because they do not divide 1710 exactly. Therefore, the correct factors from the options are 2, 5, and 10.

Explanation

Factors of a number are integers that divide the number exactly without leaving a remainder. For 1710, the factors include 2, 5, and 10 because 1710 can be divided by these numbers with no remainder (e.g., 1710 ÷ 2 = 855). However, numbers like 4, 7, and 8 are not factors of 1710 because they do not divide 1710 exactly. Therefore, the correct factors from the options are 2, 5, and 10.