SOLUTION: X is an integer greater than one such that when it is divided by 3, 5, 7, or 13, the remainder is one. What is the smallest possible value of X? a) 1363 b) 1364 c) 1365 d) 1366 e)

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Question 251680: X is an integer greater than one such that when it is divided by 3, 5, 7, or 13, the remainder is one. What is the smallest possible value of X?
a) 1363 b) 1364 c) 1365 d) 1366 e) none of these
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
x must be one more than the factors 3*5*7*13.
It must be an even number to have a remainder of one when divided by 3,5,7,13
the only even numbers options are 1364 and 1366
1364/13 has a remainder of 12
3*5*7*13+1=1366
d)1366