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Explanation A number is considered a factor of another number if it divides the other number without leaving a remainder. In this case, we need to check if 3 is a factor of 111. If we divide 111 by 3, we get 37 with no remainder. Therefore, 3 is a factor of 111.
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2.
Which of the following numbers is prime?
A.
123
B.
111
C.
131
Correct Answer C. 131
Explanation 131 is the only prime number among the given options. Prime numbers are numbers that are only divisible by 1 and themselves. In this case, 131 is not divisible by any other number except 1 and 131 itself, making it a prime number.
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3.
An even number is divisible by 2.
A.
True
B.
False
Correct Answer A. True
Explanation An even number is divisible by 2 because by definition, an even number is any integer that is exactly divisible by 2. This means that when an even number is divided by 2, there is no remainder. Therefore, the statement "An even number is divisible by 2" is true.
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4.
An odd number is always divisible by 3.
A.
True
B.
False
Correct Answer B. False
Explanation This statement is false. An odd number is not always divisible by 3. For example, the number 5 is an odd number but it is not divisible by 3.
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5.
Prime number has only one factor.
A.
True
B.
False
Correct Answer B. False
Explanation A prime number is a number greater than 1 that has only two factors, 1 and itself. Therefore, the given statement is incorrect. A prime number does not have only one factor, but rather exactly two factors.
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6.
1 is a composite number.
A.
True
B.
False
Correct Answer B. False
Explanation A composite number is a positive integer greater than 1 that has at least one divisor other than 1 and itself. Since 1 only has itself as a divisor, it is not considered a composite number. Therefore, the statement "1 is a composite number" is false.
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7.
If a number is prime, then it has at least 3 factors.
A.
True
B.
False
Correct Answer B. False
Explanation The statement is false because a prime number only has two factors, which are 1 and itself. Therefore, it does not have at least 3 factors.
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8.
2 is always a factor of even number.
A.
True
B.
False
Correct Answer A. True
Explanation This statement is true because by definition, an even number is any integer that is evenly divisible by 2. Therefore, 2 will always be a factor of any even number.
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9.
If 8 is a factor of a number, then 4 is also a factor.
A.
True
B.
False
Correct Answer A. True
Explanation If 8 is a factor of a number, it means that the number can be divided evenly by 8 without leaving a remainder. Since 8 is a factor of the number, it implies that the number is divisible by 8. Since 4 is a factor of 8 (as it can be divided evenly by 4), it follows that if 8 is a factor of a number, then 4 is also a factor. Therefore, the statement is true.
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10.
If 9 is a factor of a number, then 2 is also a factor.
A.
True
B.
False
Correct Answer B. False
Explanation This statement is false because there is no direct relationship between the factors of a number. Just because 9 is a factor of a number does not mean that 2 will also be a factor. Factors are independent of each other and can vary depending on the specific number.
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11.
If 10 is a factor of a number, then 5 is also a factor.
A.
True
B.
False
Correct Answer A. True
Explanation If 10 is a factor of a number, it means that the number can be divided evenly by 10 without leaving a remainder. Since 10 is divisible by 5, any number that is divisible by 10 will also be divisible by 5. Therefore, 5 is also a factor of the number. Hence, the statement "If 10 is a factor of a number, then 5 is also a factor" is true.
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12.
If the GCF of two numbers is 1, then the LCM is the product of two numbers.
A.
True
B.
False
Correct Answer A. True
Explanation When the greatest common factor (GCF) of two numbers is 1, it means that the two numbers do not share any common factors other than 1. In such a case, the least common multiple (LCM) of the two numbers will be the product of the two numbers. This is because the LCM is the smallest multiple that both numbers share, and since they do not have any common factors other than 1, their LCM will be their product. Therefore, the statement is true.
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13.
If the GCF of 2 numbers is odd, then both numbers are _____.
A.
Even
B.
Odd
C.
Sometimes even, sometimes odd
Correct Answer C. Sometimes even, sometimes odd
Explanation If the GCF (Greatest Common Factor) of two numbers is odd, it means that there is at least one odd factor that is common to both numbers. This implies that both numbers must have at least one odd factor in common. However, it is still possible for both numbers to have additional factors that are even and not common between them. Therefore, in this case, both numbers can be sometimes even and sometimes odd.
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14.
If the GCF of 2 numbers is even, then both numbers are _____.
A.
Even
B.
Odd
C.
Sometimes even, sometimes odd
Correct Answer A. Even
Explanation If the greatest common factor (GCF) of two numbers is even, it means that both numbers have at least one common factor that is even. This implies that both numbers must be divisible by 2, making them even numbers. Therefore, the correct answer is "Even".
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15.
The GCF of 2 numbers is always ______ their LCM.
A.
Less than
B.
Greater than
C.
Equal to
Correct Answer A. Less than
Explanation The GCF (Greatest Common Factor) of two numbers is always less than their LCM (Least Common Multiple). This is because the GCF represents the largest number that divides both numbers evenly, while the LCM represents the smallest number that is a multiple of both numbers. Since the GCF is a factor of both numbers, it will always be smaller than the LCM, which includes all the common factors and any additional factors. Therefore, the GCF is always less than the LCM.
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16.
What is the GCF of 3 and 12?
Correct Answer 3
Explanation The GCF (Greatest Common Factor) of 3 and 12 is 3 because it is the largest number that can evenly divide both 3 and 12 without leaving a remainder.
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17.
What is the GCF of 30 and 18?
Correct Answer 6
Explanation The greatest common factor (GCF) is the largest number that divides both 30 and 18 without leaving a remainder. In this case, the factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30, while the factors of 18 are 1, 2, 3, 6, 9, and 18. The largest number that appears in both lists is 6, so it is the GCF of 30 and 18.
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18.
What is the GCF of 12, 24, 72?
Correct Answer 12
Explanation The GCF (Greatest Common Factor) of a set of numbers is the largest number that divides evenly into all of the given numbers. In this case, the numbers 12, 24, and 72 can all be divided by 12 without any remainder. Therefore, 12 is the largest number that divides evenly into all three numbers, making it the GCF.
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19.
What is the GCF of 6, 32, 128?
Correct Answer 2
Explanation The greatest common factor (GCF) is the largest number that divides evenly into all the given numbers. To find the GCF of 6, 32, and 128, we can start by finding the prime factorization of each number. The prime factorization of 6 is 2 * 3, the prime factorization of 32 is 2 * 2 * 2 * 2 * 2, and the prime factorization of 128 is 2 * 2 * 2 * 2 * 2 * 2 * 2. The common factor among all three numbers is 2, which is the largest number that divides evenly into all the given numbers. Therefore, the GCF of 6, 32, and 128 is 2.
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20.
What is the LCM of 11 and 10?
Correct Answer 110
Explanation The least common multiple (LCM) of two numbers is the smallest number that is divisible by both of them. To find the LCM of 11 and 10, we can list the multiples of each number and find the smallest common multiple. The multiples of 11 are: 11, 22, 33, 44, 55, 66, 77, 88, 99, 110... The multiples of 10 are: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110... The smallest common multiple is 110, so the LCM of 11 and 10 is 110.
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21.
What is the LCM of 14 and 20?
Correct Answer 140
Explanation The LCM (Least Common Multiple) is the smallest multiple that two or more numbers have in common. To find the LCM of 14 and 20, we can list the multiples of both numbers and find the smallest one they share. The multiples of 14 are: 14, 28, 42, 56, 70, 84, 98, 112, 126, 140, ... The multiples of 20 are: 20, 40, 60, 80, 100, 120, 140, ... The smallest multiple they have in common is 140, so the LCM of 14 and 20 is 140.
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22.
What is the LCM of 3, 12 , 16?
Correct Answer 48
Explanation The least common multiple (LCM) is the smallest number that is divisible by all the given numbers. To find the LCM of 3, 12, and 16, we can list the multiples of each number and find the smallest number that appears in all three lists. The multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, ... The multiples of 12 are 12, 24, 36, 48, ... The multiples of 16 are 16, 32, 48, ... The smallest number that appears in all three lists is 48, so the LCM of 3, 12, and 16 is 48.
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23.
What is the LCM of 6, 10, 15?
Correct Answer 30
Explanation The least common multiple (LCM) is the smallest multiple that is divisible by all the given numbers. To find the LCM of 6, 10, and 15, we can start by listing the multiples of each number: 6 (6, 12, 18, 24, 30, ...) 10 (10, 20, 30, ...) 15 (15, 30, ...). The smallest number that appears in all three lists is 30, so the LCM of 6, 10, and 15 is 30.
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24.
What is the sum of the GCF and LCM of 40 and 48?
Correct Answer 248
Explanation The GCF (Greatest Common Factor) of 40 and 48 is 8, which is the largest number that divides both 40 and 48 evenly. The LCM (Least Common Multiple) of 40 and 48 is 240, which is the smallest number that is divisible by both 40 and 48. The sum of the GCF and LCM is 8 + 240 = 248.
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25.
What is the sum of the GCF and LCM of 20 and 125?
Correct Answer 505
Explanation The GCF (Greatest Common Factor) of 20 and 125 is 5, as it is the largest number that divides both 20 and 125 evenly. The LCM (Least Common Multiple) of 20 and 125 is 500, as it is the smallest number that is divisible by both 20 and 125. Therefore, the sum of the GCF and LCM of 20 and 125 is 5 + 500 = 505.
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