Question

The number of even proper divisors of `1008`

Answer 1

`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