Question

What is `753792-:832`?

Answer 1

`753792 -: 832 = 906`

Explanation:

Notice that `753792` and `832` are both divisible by `2`, so we find:

`753792 -: 832 = (color(red)(cancel(color(black)(2))) xx 376896) -: (color(red)(cancel(color(black)(2))) xx 416) = 376896 -: 416`

Then `376896` and `416` are both divisible by `2`, so we can repeat the process to find:

`753792 -: 832`

`=376896 -: 416`

`=188448 -: 208`

`=94224 -: 104`

`=47112 -: 52`

`=23556 -: 26`

`=11778 -: 13`

Does this still look a little cumbersome?

We could simply long divide it at this point, but let us factor `11778` to see what's there:

`11778`

`=2 xx 5889`

`=2 xx 3 xx 1963`

`=6 xx (1300 + 650 + 13)`

`=6 xx ((100xx13)+(50xx13)+(1xx13))`

`=6 xx ((100+50+1)xx13)`

`=6 xx 151 xx 13`

`=906 xx 13`

So `753792 -: 832 = 11778 -: 13 = 906`