Q. Which of the following is the greatest common divisor (GCD) of 48 and 180?
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Solution
The GCD of 48 and 180 is 12, as it is the largest number that divides both without a remainder.
Correct Answer:
A
— 12
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Q. Which of the following is the greatest common factor (GCF) of 48 and 180?
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Solution
The GCF of 48 and 180 is 12.
Correct Answer:
A
— 12
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Q. Which of the following is the least common multiple (LCM) of 9 and 12?
A.
36
B.
72
C.
108
D.
144
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Solution
The LCM of 9 and 12 is 36, as it is the smallest number that both can divide evenly.
Correct Answer:
A
— 36
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Q. Which of the following is the least common multiple of 8 and 12?
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Solution
The least common multiple of 8 and 12 is 24, but the next multiple is 48.
Correct Answer:
B
— 48
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Q. Which of the following is the smallest multiple of 7 that is greater than 50?
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Solution
The multiples of 7 are 7, 14, 21, 28, 35, 42, 49, 56, ... The smallest multiple greater than 50 is 56.
Correct Answer:
A
— 56
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Q. Which of the following numbers is a common multiple of 3 and 5?
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Solution
15 is the smallest common multiple of 3 and 5, and 30 is also a common multiple. However, 15 is the first one listed.
Correct Answer:
A
— 15
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Q. Which of the following numbers is a common multiple of 4 and 6?
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Solution
12 is the smallest common multiple of 4 and 6, and 24 is also a common multiple, but 12 is the smallest.
Correct Answer:
A
— 12
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Q. Which of the following numbers is a factor of 144?
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Solution
12 is a factor of 144 because 144 ÷ 12 = 12, which is an integer.
Correct Answer:
B
— 12
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Q. Which of the following numbers is a factor of 48?
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Solution
12 is a factor of 48, as 48 divided by 12 equals 4, which is an integer.
Correct Answer:
B
— 12
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Q. Which of the following numbers is a factor of 60?
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Solution
12 is a factor of 60 as 60 divided by 12 equals 5 with no remainder.
Correct Answer:
B
— 12
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Q. Which of the following numbers is a multiple of both 4 and 6?
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Solution
12 is the smallest number that is a multiple of both 4 and 6.
Correct Answer:
A
— 12
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Q. Which of the following numbers is NOT a factor of 60?
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Solution
7 is not a factor of 60, as 60 cannot be divided evenly by 7.
Correct Answer:
D
— 7
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Q. Which of the following numbers is NOT a multiple of 11?
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Solution
50 is not a multiple of 11, while the others are.
Correct Answer:
D
— 50
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Q. Which of the following numbers is NOT a multiple of 6?
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Solution
35 is not a multiple of 6, while 18, 24, and 30 are all multiples of 6.
Correct Answer:
D
— 35
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Q. Which of the following pairs of numbers has a GCD of 1?
A.
8 and 12
B.
15 and 28
C.
9 and 27
D.
10 and 20
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Solution
15 and 28 have no common factors other than 1, making their GCD equal to 1.
Correct Answer:
B
— 15 and 28
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Q. Which of the following pairs of numbers has a greatest common divisor (GCD) of 1?
A.
8 and 12
B.
15 and 28
C.
9 and 27
D.
10 and 20
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Solution
15 and 28 are coprime, meaning their GCD is 1.
Correct Answer:
B
— 15 and 28
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Q. Which of the following pairs of numbers has a least common multiple (LCM) of 36?
A.
6 and 12
B.
4 and 9
C.
3 and 18
D.
2 and 18
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Solution
The LCM of 4 and 9 is 36.
Correct Answer:
B
— 4 and 9
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Q. Which of the following pairs of numbers has the greatest common factor (GCF) of 1?
A.
8 and 12
B.
15 and 28
C.
9 and 27
D.
14 and 21
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Solution
The GCF of 15 and 28 is 1, making them coprime, while the other pairs share common factors.
Correct Answer:
B
— 15 and 28
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Q. Which of the following statements about factors and multiples is correct? (2023)
A.
Every multiple of a number is also a factor of that number.
B.
Factors of a number are always greater than the number itself.
C.
A number can have an infinite number of multiples.
D.
The smallest multiple of any number is always the number itself.
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Solution
A number can have an infinite number of multiples, as you can keep adding the number to itself indefinitely.
Correct Answer:
C
— A number can have an infinite number of multiples.
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Q. Which of the following statements about factors and multiples is incorrect? (2023)
A.
Every multiple of a number is greater than or equal to that number.
B.
A number can have an infinite number of factors.
C.
The product of two numbers is always a multiple of both.
D.
A factor of a number is always greater than the number.
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Solution
A factor of a number is always less than or equal to that number, making the last statement incorrect.
Correct Answer:
D
— A factor of a number is always greater than the number.
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Q. Which of the following statements about factors is incorrect?
A.
Every number has at least two factors.
B.
Factors can be negative.
C.
The number itself is always a factor.
D.
Factors of a prime number are only 1 and the number itself.
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Solution
Every number has at least two factors: 1 and the number itself, but some numbers can have more than two factors.
Correct Answer:
A
— Every number has at least two factors.
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Q. Which of the following statements about multiples is true?
A.
The multiples of a number are infinite.
B.
The multiples of a number are always positive.
C.
The first multiple of any number is the number itself.
D.
All of the above.
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Solution
All statements are true regarding multiples.
Correct Answer:
D
— All of the above.
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Q. Which of the following statements about the number 30 is true?
A.
It is a prime number
B.
It has exactly 4 factors
C.
It is a multiple of 5
D.
It is not a composite number
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Solution
30 is a multiple of 5, as it can be expressed as 5 multiplied by 6.
Correct Answer:
C
— It is a multiple of 5
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Q. Which of the following statements is logically consistent with the definition of multiples?
A.
Every multiple of 7 is also a multiple of 14.
B.
A number cannot be a multiple of itself.
C.
The sum of two multiples of 3 is always a multiple of 3.
D.
A multiple of 5 is never a multiple of 10.
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Solution
The sum of two multiples of 3 is always a multiple of 3, as multiples of a number are closed under addition.
Correct Answer:
C
— The sum of two multiples of 3 is always a multiple of 3.
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Q. Which of the following statements is logically consistent with the definition of a multiple?
A.
A multiple of a number is always greater than the number itself.
B.
A multiple of a number can be negative.
C.
A multiple of a number is always an integer.
D.
All of the above.
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Solution
All statements are true; multiples can be negative, can be equal to the number, and are always integers.
Correct Answer:
D
— All of the above.
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Q. Which of the following statements is logically consistent with the definition of a factor?
A.
A factor of a number is always greater than the number.
B.
A factor of a number divides the number without leaving a remainder.
C.
A factor can only be a prime number.
D.
A factor is always a multiple of the number.
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Solution
By definition, a factor divides the number evenly, leaving no remainder.
Correct Answer:
B
— A factor of a number divides the number without leaving a remainder.
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Q. Which of the following statements is logically consistent with the properties of factors?
A.
Every factor of a number is also a multiple of that number.
B.
A number can have an infinite number of factors.
C.
The smallest factor of any number is always 1.
D.
All prime numbers have exactly two factors.
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Solution
The smallest factor of any number is always 1, as 1 divides every integer.
Correct Answer:
C
— The smallest factor of any number is always 1.
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Q. Which of the following statements is true regarding factors and multiples?
A.
All factors are multiples.
B.
All multiples are factors.
C.
Factors are always less than multiples.
D.
Multiples are always less than factors.
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Solution
Factors of a number are the integers that can divide that number without leaving a remainder, while multiples are the result of multiplying that number by an integer. Hence, factors are always less than or equal to multiples.
Correct Answer:
C
— Factors are always less than multiples.
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Q. Which of the following statements is true regarding prime numbers? (2023)
A.
Every prime number is a multiple of 1.
B.
Prime numbers have exactly two distinct positive divisors.
C.
All even numbers are prime.
D.
The number 1 is a prime number.
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Solution
Prime numbers are defined as having exactly two distinct positive divisors: 1 and the number itself.
Correct Answer:
B
— Prime numbers have exactly two distinct positive divisors.
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Q. Which of the following statements is true regarding the factors of 36?
A.
36 has 8 factors
B.
36 is a prime number
C.
All factors of 36 are even
D.
36 is a perfect square
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Solution
36 is indeed a perfect square as it can be expressed as 6 x 6.
Correct Answer:
D
— 36 is a perfect square
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