We now divide 74 by 29.
We divide 74 by 10 to get 7 (we just drop the last digit to get an approximate answer), and then divide
by 3. Three divides into 7 twice, so 2 is the next digit of our answer.
Multiply 2 by 29 to get 58 (twice 30 minus 2), and then subtract from 74. The answer is 16. Then we
bring down the 5, writing the X below.
We now divide 165 by 29.
Roughly dividing 169 by 10 we get 16. Sixteen divided by 3 is 5.
Multiply 29 by 5 to get 145. Subtract 145 from 165 for a remainder of 20.Our answer is 425 with 20 remainder. The calculation is done. Our only real division was by 3.
Long division is easy if you regard the problem as an exercise with factors. Even though we are
dividing by a prime number, we make our estimates by rounding off and using factors.
The general rule for standard long division is this:
Round off the divisor to the nearest ten, hundred or thousand to make an easy estimate.
If you are dividing by 31, round off to 30 and divide by 3 and 10.
If you are dividing by 87, round off to 90 and divide by 9 and 10.
If you are dividing by 321, round off to 300 and divide by 3 and 100.
If you are dividing by 487, round off to 500 and divide by 5 and 100.
If you are dividing by 6,142, round off to 6,000 and divide by 6 and 1,000.
This way, you are able to make an easy estimate and then proceed in the usual way.
Remember that these calculations are really only estimates. If you are dividing by 31 and you make
your estimate by dividing by 30, the answer is not exact — it is only an approximation. For instance,
what if you were dividing 241 by 31?
You round off to 30 and divide by 10 and by 3.
Two hundred and forty-one divided by 10 is 24. We simply drop the 1.
Twenty-four divided by 3 is 8.
We multiply 8 times 31 and subtract the answer from 241 to get our remainder.
Eight times 31 is 248. This is greater than the number we are dividing so we cannot subtract it. Our
answer was too high. We drop to 7.
Seven times 31 is 217.