jmc

Question

The number 210 is the product of two consecutive positive integers and is also the product of three consecutive integers. What is the sum of those five integers?

Accepted Answer

First we prime factorize 210=2357. Trying some pairwise products of these primes, we see that 210=(27)(35)=1415. Also, 210=(5)(23)(7)=567. The sum of the five integers is 14+15+5+6+7=47.