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?
I need to find two pairs of numbers that multiply to 210, one pair being consecutive and the other being three consecutive numbers. I notice that 15 and 14 are consecutive factors of 210, so that's one pair. I also notice that 5, 6, and 7 are consecutive factors of 210, so that's another pair. The sum of the five integers is 15 + 14 + 5 + 6 + 7 = 47. 