The product of ages of a group of teenagers is 705600. find number of teenagers in group n sum of their ages??

This is a problem in Diophantine analysis. We must find a solution in whole numbers, presumably from 13 to 19.





First, prime factor 705600.





705600 = 2^6 3^2 5^2 7^2





With the 7 and the 5, there is only 1 choice available.





7 * 2 = 14


5 * 3 = 15





Rewrite, taking out the factors we have used.





705600 = 2^4 * 14^2 * 15^2





All that's left is the 2^4 =16





705600 = 16 * 14^2 * 15^2





The 5 teenagers are ages 14, 14, 15, 15, and 16.





14 * 14 * 15 * 15 * 16 = 705600





The sum of their ages is





14 + 14 + 15 + 15 + 16 = 74The product of ages of a group of teenagers is 705600. find number of teenagers in group n sum of their ages??
Is that the full question... Can you give me more detail...