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Explanation A prime number has only two factors, which are 1 and the number itself. This means that a prime number cannot be divided evenly by any other number except for 1 and itself. For example, the factors of the prime number 5 are 1 and 5, and there are no other factors. Therefore, the correct answer is 2.
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2.
What are the first three prime numbers?
A.
0, 1, 2
B.
1, 2, 3
C.
2, 3, 5
Correct Answer C. 2, 3, 5
Explanation The first three prime numbers are 2, 3, and 5. Prime numbers are numbers that are only divisible by 1 and themselves. 0 and 1 are not prime numbers because they have additional divisors. 2 is the smallest prime number, followed by 3 and then 5. Therefore, the correct answer is 2, 3, 5.
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3.
How many primes are even numbers?
A.
1
B.
0
C.
All
Correct Answer A. 1
Explanation Primes are numbers that are only divisible by 1 and themselves. However, the only even prime number is 2. All other even numbers are divisible by 2 and therefore not prime. Therefore, the correct answer is 1.
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4.
Which set of numbers are all Primes?
A.
33, 29, 41, 3
B.
63, 71, 43, 81
C.
5, 23, 11, 37
Correct Answer C. 5, 23, 11, 37
Explanation The set of numbers 5, 23, 11, and 37 are all prime numbers. A prime number is a number that is only divisible by 1 and itself, and none of these numbers have any other divisors. Therefore, they are all prime numbers.
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5.
The factors of 18 are 1, 2, 3, 6, 9, 18.
A.
True
B.
False
Correct Answer A. True
Explanation The statement is true because the factors of 18 are indeed 1, 2, 3, 6, 9, and 18. Factors are numbers that can divide evenly into another number without leaving a remainder. In this case, all of the listed numbers can divide 18 without leaving a remainder, making them factors of 18.
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6.
The Prime Factors of 18 are 1, 2, 3.
A.
True
B.
False
Correct Answer B. False
Explanation 1 is not a prime.
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7.
What are the prime factors of 32?
A.
2
B.
2, 8, 16
C.
1, 2, 4, 8, 16, 32
Correct Answer A. 2
Explanation The prime factors of 32 are the numbers that can divide 32 without leaving a remainder and are also prime numbers. In this case, the only prime factor of 32 is 2, because 32 can be divided evenly by 2.
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8.
Is 7 a prime factor of 84?
A.
True
B.
False
Correct Answer A. True
Explanation A prime factor is a prime number that divides another number without leaving a remainder. To determine if 7 is a prime factor of 84, we need to check if 7 divides 84 evenly. By dividing 84 by 7, we get a quotient of 12 with no remainder. Therefore, 7 is a prime factor of 84.
Explanation The factors of a number are the numbers that divide evenly into that number without leaving a remainder. To find the factors of 84, we can start by dividing it by the smallest prime number, which is 2. 84 divided by 2 equals 42, so 2 is a factor of 84. Continuing this process, we divide 42 by 2 to get 21, which means 2 is a factor again. We repeat this process with the remaining factors until we reach the largest prime factor, which is 7. Therefore, the factors of 84 are 1, 2, 3, 4, 7, 12, 21, 28, 42, and 84.
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10.
What are the prime factors of 84?
A.
2, 3, 7
B.
1, 2, 4, 21, 42, 84
C.
1, 2, 3, 4, 7, 12, 21, 42, 84
D.
1, 2, 3, 4, 7, 12, 21, 28, 42, 84
Correct Answer A. 2, 3, 7
Explanation The prime factors of a number are the prime numbers that divide the number evenly. To find the prime factors of 84, we can divide it by prime numbers starting from 2. 84 divided by 2 is 42, which is still divisible by 2, resulting in 21. 21 is not divisible by 2, so we move on to the next prime number, which is 3. 21 divided by 3 is 7, and 7 is a prime number. Therefore, the prime factors of 84 are 2, 3, and 7.
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11.
9 is a Prime Factor of 81.
A.
True
B.
False
Correct Answer B. False
Explanation A prime factor is a prime number that divides another number without leaving a remainder. The prime factors of 81 are 3 and 3, since 3 x 3 x 3 = 81. Therefore, 9 is not a prime factor of 81.
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12.
3 is the ONLY prime factor of 81.
A.
True
B.
False
Correct Answer A. True
Explanation The statement is true because 3 is indeed the only prime factor of 81. A prime factor is a prime number that divides another number without leaving a remainder. In the case of 81, it can be expressed as 3 x 3 x 3, where 3 is the only prime factor. There are no other prime numbers that can divide 81 evenly. Therefore, the answer is true.
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13.
The prime factors of 75 are:
A.
1, 3, 5
B.
3, 5
C.
1, 3, 5, 15, 25, 75
Correct Answer B. 3, 5
Explanation The prime factors of a number are the prime numbers that can divide the number without leaving a remainder. In this case, the prime factors of 75 are 3 and 5. This is because 3 and 5 are both prime numbers and they can both divide 75 without leaving a remainder. Therefore, the prime factors of 75 are 3 and 5.
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14.
The prime factor of 193 is only 193.
A.
True
B.
False
Correct Answer A. True
Explanation The prime factors of a number are the prime numbers that can divide the given number evenly without leaving a remainder. In this case, the number 193 only has two factors, 1 and 193. While 1 is not a prime number, 193 is. Therefore, the statement "The prime factor of 193 is only 193" is true.
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