Question

What are the factors of 1008?

Answer 1

easiest way to figure this out is to prime factorize:
1008 / 2 = 504
504 / 2 = 252
252 / 2 = 126
126 / 2 = 63
63 / 7 = 9
9 / 3 = 3

so the prime factorization becomes:

\[2^4*3^2*7\]

then you need to use combinations of those numbers to find the factors:
\[ 2 * 504 = 2 * (2^3*3^2*7)\]
\[3 * 336 = 3 * (2^4*3*7)\]
\[4 * 252 = 2^2 * (2^2*3^2*7)\]
\[6 * 168 = (2*3) * (2^3*3*7)\]
\[7 * 144 = 7 * (2^4*3^2)\]
\[8 * 126 = 2^3 * (2*3^2*7)\]
\[9 * 112 = 3^2 * (2^4*7)\]
\[12 * 84 = (2^2*3) * (2^2*3*7)\]
\[14 * 72 = (2*7) * (2^3*3^2)\]
\[16 * 63 = 2^4 * (3^2*7)\]
\[18 * 56 = (2*3^2) * (2^3*7)\]
\[21 * 48 = (3*7) * (2^4*3)\]
\[24 * 42 = (2^3*3) * (2*3*7)\]
\[28 * 36 = (2^2*7) * (2^2*3^2)\]

you know you are done when you can't find any more combinations below the squareroot of 1008, which is about 31.74.