## SIR 2 years ago N=12*12*12*3*3*3*3*5*5,then the total number of even factor of N is

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1. shubhamk

Split the number N into prime factors and then obtain the even factors using simple combinatorics. I see 126 unique even divisors.

2. eliassaab

$N=2^6 3^7 5^2$

3. eliassaab

To have an even factor the 2 must always occur in the factor. So the even factors are of the form $2^m 3^n 5^p; \quad 1\leq m \leq 6; \quad 0\leq n \leq 7; \quad 0\leq m \leq 2$ How many are there?

4. eliassaab

There are 6* 8* 3= 144

5. eliassaab

Here a list of the 144 {2, 4, 6, 8, 10, 12, 16, 18, 20, 24, 30, 32, 36, 40, 48, 50, 54, 60, \ 64, 72, 80, 90, 96, 100, 108, 120, 144, 150, 160, 162, 180, 192, 200, \ 216, 240, 270, 288, 300, 320, 324, 360, 400, 432, 450, 480, 486, 540, \ 576, 600, 648, 720, 800, 810, 864, 900, 960, 972, 1080, 1200, 1296, \ 1350, 1440, 1458, 1600, 1620, 1728, 1800, 1944, 2160, 2400, 2430, \ 2592, 2700, 2880, 2916, 3240, 3600, 3888, 4050, 4320, 4374, 4800, \ 4860, 5184, 5400, 5832, 6480, 7200, 7290, 7776, 8100, 8640, 8748, \ 9720, 10800, 11664, 12150, 12960, 14400, 14580, 15552, 16200, 17496, \ 19440, 21600, 21870, 23328, 24300, 25920, 29160, 32400, 34992, 36450, \ 38880, 43200, 43740, 46656, 48600, 58320, 64800, 69984, 72900, 77760, \ 87480, 97200, 109350, 116640, 129600, 139968, 145800, 174960, 194400, \ 218700, 233280, 291600, 349920, 388800, 437400, 583200, 699840, \ 874800, 1166400, 1749600, 3499200}