The product of two multiples of 7 is 7007. What is their sum? What's the best way to figure this out?

Question

What's the simplest way to figure out a question like this?

Answer 1

Divide 7007 by 7 to get 1001 and then add 1001 and 7 to get 1008.

Answer 2

In Elementary Math, you could look at 7007 and realize that it is 7*1001. 7 is a multiple of 7 [that is, 7*1], but is 1001 a multiple of 7? Well, yes, 1001 = 7*143.

So, 1001 = 7 * 1001 and their sum is 7+1001 = 1008

Ah, but there is more!

7007 = 1001*7 = (7*11*13)*7

Later, you will learn about prime numbers (are the product of only 1 and themselves) and composite numbers (may be the product of other numbers also). For example, 5 is prime, but 8 is not (because 8 = 1*8 = 2*4 = 2*2*2).

The prime factors of:

7 are 1, 7 -- it is prime

7007 are 7, 7, 11, 13 --- it is composite

Now, what "multiples of 7" can we make from those factors"

7*7 = 49 times 143 is 7007

7*11 = 77 times 91 is 7007

7*13 = 91 times 77 is 7007

7*7*11 = 539 times 13 is 7007

7*7*13 = 637 times 11 is 7007

Now, you may choose any pair from that list.

49 and 143 are multiples of 7 and their sum is 192.