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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....

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....

Grade:12

1 Answers

AJIT AskiitiansExpert-IITD
68 Points
10 years ago

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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