Peter notices that the teenage students who are members of the math club have ages whose product is 611520. How many members does the club have?

Question

Extensions: Is it true that whatever number replaces 611520 that this problem has a unique solution? Suppose the club included 12 year olds and the product was
163762560, how many members does the club now have

Answer 1

I tried dividing the given number by number that reflect teenagers.
That is, I started with 13
61150 = 13*47040
47040 = 14*3360
3360=15*224
224=14*16

so the factors are:
13*14*14*15*16
So there are 5 factors, thus 5 members in the club

For the second part, start with 12, then use my method
(hint your number divides by 12 evenly three times)

Answer 2

If you have 12 year olds, you can switch around 12, 16, and 18 year olds. There isn't always a unique solution for if 12 is included.

Answer 3

c) 163 762 560= 2^7*3^9*5*13
1-13 yr-old
2-12 yr-old
3-18 yr-old
1-15 yr-old
=7 members