The following question has two parts. First, answer part A. Then, answer part B.

Question

Part A
Martina is trying to find a factor pair for the number 62. She says that because 62 is an even number, then 2 has to be one of the factors in a factor pair.

Do you agree with Martina's reasoning? If you agree, find the missing factor. If you disagree, find another factor pair for 62. In either case, make sure you explain how you use one factor to find the other factor in the pair.

(2 points)

Question 2
Part B
Lucas says that 15 is both a prime number and a composite number.

State whether you agree or disagree with Lucas, and be sure to give a definition of either a prime or composite number to strengthen your argument.

(2 points)

Answer 1

Part A

I agree with Martina's reasoning that since 62 is an even number, 2 must be one of the factors in a factor pair. To find the missing factor, we can divide 62 by 2:

\[ 62 \div 2 = 31 \]

Therefore, one factor pair for 62 is (2, 31). In this pair, 2 is a factor, and 31 is the other factor that, when multiplied by 2, gives 62:

\[ 2 \times 31 = 62 \]

Part B

I disagree with Lucas's statement that 15 is both a prime number and a composite number.

A prime number is defined as a number greater than 1 that has no positive divisors other than 1 and itself. In contrast, a composite number is a number greater than 1 that has more than two positive divisors.

Since 15 has divisors of 1, 3, 5, and 15, it can be divided evenly by numbers other than 1 and itself (specifically 3 and 5). Thus, 15 meets the definition of a composite number, but it does not qualify as a prime number because it has more than two distinct factors. Therefore, 15 is solely a composite number.