# Divide two number in base 7: `((252)_7)/5_7`

justaguide | Certified Educator

Two numbers in base 7 can be divided in a manner similar to how two numbers in base 10 can be divided.

Numbers in base 7 are only made up of the digits 0, 1, 2, 3, 4, 5 and 6. The division is a little difficult as people do not learn the multiplication tables of numbers in base 7. For instance in the base 7 system: `5_7*1_7 = 5_7` , `5_7*2_7 = 13_7` , `5_7*3_7 = 21_7` , `5_7*4_7 = 26_7` , `5_7*5_7 = 34_7`, `5_7*6_7 = 42_7` ...

Dividing `252_7` by `5_7` could be accomplished as follows:

`5_7` | `252_7` | `(3_7)(6_7)`

.......`21_7`

-----------------------

.........`42_7`

........`42_7`

-------------------------

...........`0_7`

The result of the division of `252_7` by `5_7` is `36_7`

jeew-m | Certified Educator

To divide this you have to convert this base 7 to base 10.

If you say 252 base 10 that means;

252 = 2*10^2+5*10^1+2^10^0

= 200+50+2

The Right side is always in base 10.

252 (base 7) = 2*7^2+5*7^1+2*7^0 = 98+35+2 = 135 (base 10)

5 base (7) = 5*7^0 = 5(base 10)

Now 252 (base 7)/5 base (7) = 135 (base 10)/5(base 10)

= 27 (base 10)

Now we have to convert 27 (base 10) to base 7.

27 (base 10) = 3*7^1+6*7^0

= 36 (base 7)

Therefore;

252 (base 7)/5 base (7) = 36 (base 7)