SOLUTION: n,a are natural numbers each greater than 1. If a+a+a.....+a=2010 and there are nth terms in the left side . Then the number of ordered pairs(a,n) = ?

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Question 474942: n,a are natural numbers each greater than 1. If a+a+a.....+a=2010 and there are nth terms in the left side . Then the number of ordered pairs(a,n) = ?
Found 2 solutions by robertb, richard1234:
Answer by robertb(5830) About Me  (Show Source):
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Simply the number of factors of 2010. We can have {a,n} = {1,2010}, {2,1005}, ..., {2010, 1}. 2010 (=2*3*5*67) has 16 factors so there are 16 ordered pairs. However we have to subtract {1,2010} and {2010,1} because n,a > 1, so 14 ordered pairs satisfy the condition.