Steps in Learning How to Do Long Division With Bases Other Than 10

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Doing computations in a base other than ten can seem complicated, because you have always worked in base ten. Performing long division involves estimation, multiplication and subtraction, but the process is simplified by all the common math facts you have memorized since early elementary school. Since those math facts often do not apply in bases other than ten, you have to find ways to compensate for the disadvantage.

    List the single-digit multiples of the divisor in the new base. As an example, here is a division problem in base seven. If you were dividing 1431 (base 7) by 23 (base 7), you would first list 23 x 1=23, 23 x 2=46, 23 x 3=102, 23 x 4=125, 23 x 5=151 and 23 x 6=204. Since you are working in base seven you do not need to multiply the divisor by more than 6. This eases the disadvantage of not knowing the multiplication facts in that base. If you were working with a different base, you would list other multiples

    Choose the highest multiple that is not greater than the leading digits of the dividend. In the example, 125 would be the appropriate multiple, since 151 and 204 are both greater than 143. Write “4” above the dividend, since 23 (base 7) times 4 is 125 (base 7).

    Subtract the appropriate multiple from the leading digits of the dividend. In the example, 143 (base 7) minus 125 (base 7) is 15 (base 7).

    Bring down any trailing digits. In this example, bring down the "1" to make the temporary remainder 151 (base 7).

    Repeat the steps until the remainder is less than the divisor. From the list of multiples, 23 x 5=151, so write “5” above the dividend to the right of the 4, and subtract 151 from 151, which leaves you with zero.

    Write down any remainder greater than zero to the right of the answer, preceded by a capital “R.” In the example, the final remainder is zero, so there is no need to specify any remainder. The final answer to 1431 (base 7) divided by 23 (base 7) is 45 (base 7).

    Tips

    • When finding multiples and subtracting from the dividend, always remember that you are not working in base ten, so the usual multiplication facts may not apply. You can check your answer by converting the divisor, dividend, and answer to base ten. A calculator will probably not give the correct answer in the base you are using, unless it is capable of doing computations in bases other than ten. When working with bases larger than ten, remember that other symbols (such as the alphabet) will have to serve for digits for 11, 12, etc.

References

About the Author

Talmadge Walker is a former schoolteacher turned professional writer. He has a bachelor's degree from Birmingham-Southern College and a master's degree in special education from Elon University. Talmadge is a volunteer historic interpreter at the Bennett Place State Historic Site.

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