1(1+7)(1+4)(1+3)(23)-2
=1278
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....
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6 Answers
1the number of ways of selecting at least one object out of n identical objects is n [1]
66Look at the terms in the expansion
(1 + a + a2 + a3 + a4 + a5 + a6 + a7) (1 + b + b2 + b3 + b4) (1 + c + c2 + c3) (1 + d) (1 + e) (1 + f)
You can easily see that each term of this expansion will be a factor of the given number N = a7b4c3def and conversely any factor of the given number must be one of these. Accordingly there are same number of factors of N as the number of terms in this expansion which is 8 X 5 X 4 X 2 X 2 X 2 = 1280
But this number includes 1 and N as well so remove 2 giving the total number of factors as 1278.