1.
Which of the following are factors of 1710?
Correct Answer
C. 2,5,10
Explanation
The factors of 1710 are the numbers that can divide 1710 without leaving a remainder.
From the options provided:
- 2 is a factor of 1710 because 2 * 855 = 1710.
- 5 is a factor of 1710 because 5 * 342 = 1710.
- 10 is a factor of 1710 because 10 * 171 = 1710.
So, the factors of 1710 are 2, 5, and 10.
2.
Which number is a multiple of 6?
Correct Answer
D. 42
Explanation
A number is considered a multiple of 6 if it can be divided by 6 without leaving a remainder. In this case, 42 can be divided by 6, resulting in an even quotient of 7. Therefore, 42 is a multiple of 6.
3.
What is the greatest common factor of 10 and 45?
Correct Answer
C. 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?
Correct Answer
B. 15
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.
Which pair of numbers has 60 as their least common multiple?
Correct Answer
A. 12 and 30
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.
6.
A number is a multiple of 6 if ________________________
Correct Answer
D. The sum of all its digits is divisible by 3 and the last digit is even
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 two numbers are relatively prime?
Correct Answer
A. 9 and 16
Explanation
Two numbers are relatively prime if they have no common factors other than 1. In this case, the numbers 9 and 16 are relatively prime because they do not share any common factors other than 1.
8.
How many multiples does 10 have?
Correct Answer
D. 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".
9.
Which number is a factor of 111?
Correct Answer
A. 3
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.
10.
What is the greatest common factor of 12 and 18?
Correct Answer
C. 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.