stevecultt wrote:If s is the sum of all integers from 1 to 30, inclusive, what is the sum of all the factors of s?
(A) 303
(B) 613
(C) 675
(D) 737
(E) 768
OA E
First let's find s. 1 to 30 inclusive is an evenly spaced set, so we know that the average = (high + low)/2 = (30 + 1)/2 = 15.5
Sum = Average * Number of terms = 15.5 * 30 = 465
Prime factorization of 465 = 3 * 5 * 31
Now we can build all of 465's factors from those prime bases: 1, 3, 5, 3*5, 31, 3*31, 5*31, 465
Clean it up: 1, 3, 5, 15, 31, 93, 155, 465
Add 'em to get 768
(or simply see that the units' digit would be '8.'
The answer is
E
