AnswersBasic Intermediate Algebra Sem. 1Prime Numbers and Prime Factorization

Prime Numbers and Prime Factorization Answers

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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.
3

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.
4

Lina and Josh each made a factor tree to find the prime factorization of 126. Lina’s Solution Josh’s Solution Which statement explains the accuracy of the students’ work?

Question illustration
A
Lina’s solution is correct because it expresses 126 as a product of prime factors.
B
Josh’s solution is correct because the factor tree of every even number must begin with 2 and its factor pair.
C
Both solutions are correct because they both express 126 as a product of factors.
D
Neither solution is correct because the factor tree should have begun with 6 and 21.
5

Which list shows all the factors of 18?

A
1, 2, 3, 4, 6, 9, 18
B
1, 2, 3, 6, 9, 18
C
2, 3, 4, 6, 9
D
2, 3, 6, 9
7

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.
8

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.
10

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

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