how do you solve 5062 base seven divided by 6 base seven

Question

need help solving 5062 base seven divided by 6 base seven

Answer 1

6₇ is just 6. One way to do the division is to convert 5062₇ to decimal.

Another way is to divide progressively by 6, remembering that a "ten" in base 7 is 7.

So since 6 doesn't divide into 5 we take the first two digits and convert to decimal:

50=5×7+0=35. 35➗6=5 rem 5. The first digit of the quotient is 5.

Now multiply the remainder by 7: 7×5=35 and add on the next digit, which is 6: 35+6=41.

Divide 41 by 6 and we get 6 rem 5, so the next digit in the quotient is 6. So far we have 56 as the first two digits of the quotient.

Now multiply the remainder by 7: 7×5=35 and add on the last digit, which is 2: 35+2=37.

Divide 37 by 6 and we get 6 rem 1, so the last digit in the quotient is 6, making it 566 rem 1.

566 is also to base 7.