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

Answer 1

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

62 ÷ 2 = 31

So, the factor pair for 62 is (2, 31). This means that 62 can be expressed as the product of these two factors: 2 × 31 = 62.

Part B: Another way to find a factor pair for 62 is to look for factors that are not 2. We can do this by checking for divisibility with other numbers.

Let's check by testing 1, 3, 4, 5, 6, ... up to the square root of 62 (which is approximately 7.87).

• 62 ÷ 1 = 62 (so, the factor pair is (1, 62))
• 62 ÷ 3 = not a whole number
• 62 ÷ 4 = not a whole number
• 62 ÷ 5 = not a whole number
• 62 ÷ 6 = not a whole number
• 62 ÷ 7 = not a whole number

Since the only pairs we find (besides using 2) is (1, 62), we can conclude that the factor pairs for 62 are (1, 62) and (2, 31). Thus, 62 can be expressed as the product of 1 and 62 or as the product of 2 and 31.