Prime Numbers and Prime Factorization Answers

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1
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Which is a true statement about the number 1?

A
One is a factor of every whole number since every number is divisible by itself.
B
One is not a factor of any number because it is neither a prime number nor a composite number.
C
One is a prime number because it has less than two factors.
D
One is a composite number because it has more than two factors.
2
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What is the prime factorization of 40?

A
2 times 5
Option A
B
2 times 20
Option B
C
2 times 2 times 2 times 5
Option C
D
2 times 2 times 4 times 5
Option D
3

Composite numbers have

A
less than two factors.
B
more than two factors.
C
exactly two factors.
D
greater than or equal to two factors.
4

Rathan thinks all factors of even numbers are even. Is Rathan correct or incorrect?

A
He is correct because the product of 2 and any number is odd.
B
He is correct because the product of two even numbers is even.
C
He is incorrect because the product of an even number and an odd number is even.
D
He is incorrect because the product of two odd numbers is odd.
7

Manuel created a factor tree and wrote the prime factorization of 60 shown below. What is Manuel’s error?

Question illustration
A
He did not include 15 in the prime factorization.
B
He did not find the prime factors of 4.
C
He should have started the factor tree with .
Option C
D
He should not have found the factors of 15.
8

The prime factorization of a number is . Which is a true statement about the factors of the number?

Question illustration
A
Fifteen is a factor of the number because both 3 and 5 are prime factors.
B
Fifteen is not a factor of the number because 15 is odd and the number is even.
C
Sixteen is a factor for the number because and 16 is divisible by 8.
Option C
D
Sixteen is not a factor of the number because the exponent of 2 is not even.
9

The prime factorization of a number is . Which statement is true about the factors of the number?

Question illustration
A
Twenty-one is a factor of the number because both 3 and 7 are prime factors.
B
Twenty-one is not a factor of the number because 21 is not prime.
C
Ninety is a factor of the number because and 90 is divisible by 9.
Option C
D
Ninety is not a factor of the number because 90 is not divisible by 7.

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