find the no. of factors ( excluding 1 and the expression itself ) of the product of a^7 b^4 c^3 d e f where a b c d e f r all prime nos..??plzzz provide the full soln....

Dear Akhil ,

consider the expression
(1 + a + a² + a³ + a⁴ + a⁵  + a⁶ + a⁷) (1 + b + b² + b³ + b⁴) (1 + c + c² + c³) (1 + d) (1 + e) (1 + f)

If you observe the expression , you will find that each term in the expansion is a factor of N = a⁷b⁴c³def .  Also the expansion starts from 1 and ends at the number itself  , in between all the factors of numbers are located . so if we can find out the number of terms in the expansion -2 (for 1 and number itself) , we will get the answer, which can be easily seen as  8 X 5 X 4 X 2 X 2 X 2 = 1280 -2 = 1278

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