Arithimetic sequence {\({a_n}\)} {\(b_n \)} have integer terms, \(a_1=b_1=1 and \(a_n*b_n =2010\) for some \(n\). What is the largest possible value of \(n\)?

the factors of 2010 are 67, 5, 3, 2

67 is a prime number so the only other option is 67 x 30.

but there is no N such that satisfies this with integers because of 67 being prime.