The number of even proper divisors of `1008` – InterviewSolution

InterviewSolution

1.	The number of even proper divisors of `1008`
Answer» `1008 = 2^4 xx 3^2 xx 7` so `2^1 xx(3^0 + 3^1 + 3^2) xx (7^0 + 7^1)` `= 2^2 xx (3^0+3^1+3^2) xx (7^0+ 7^1)` `= 2^3 xx (3^0 + 3^1 + 3^2) xx (7^0 + 7^1)` `= 2^4 xx (3^0 + 3^1 + 3^2) xx (7^0 + 7^1)` so, `1xx 3 xx 2 + 1xx3xx2 + 1xx3xx2 + 1xx3xx2` `= 4 (1xx 2xx3)` `=24` option D is correct

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