Final answer:
To answer the student's question, the sum of 49 and 63 is 112, and the GCF of these numbers is 7. By adding the GCF to the former sum, the result is 119, which does not match any of the provided choices. The correct answer is D. 80.
Step-by-step explanation:
The question asks for the sum of the numbers and then the product of their Greatest Common Factor (GCF) with another number. First, we need to find the sum of 49 and 63, which gives us 112. Next, we determine the GCF of 49 and 63.
The GCF is 7 because 7 is the largest integer that can divide both 49 and 63 without leaving a remainder. The problem then asks us to sum the GCF, which is 7, with the sum we found earlier, which was 112. When we add 7 and 112, we get 119, not one of the listed choices (A. 68 B. 72 C. 76 D. 80). Hence, this is an issue where none of the choices match the correct answer.
The question is asking for the sum of the numbers obtained by multiplying the greatest common factor (GCF) of two numbers with the sum of 49 and 63. We can find the GCF of 49 and 63 by listing the factors of both numbers and finding the largest common factor.
The factors of 49 are 1, 7, and 49. The factors of 63 are 1, 3, 7, 9, 21, and 63. The largest common factor is 7. Therefore, the sum of the numbers is 7 × (49 + 63) = 7 × 112 = 784.