How To Convert Base 10 To Other Bases

Converting from base 10 to other bases, including to base 2, requires the use of a method called “repeated division.”

In this lesson, you will learn the step-by-step method of using repeated division to convert base 10 to other bases.

BONUS: A link to practice questions on number bases is included at the end of this lesson.

Question on converting base 10 to other bases

Let’s take an example:

Question:

Convert 7410 to a number in base 5

STEP 1.

Draw a table that looks like “T”

STEP 2.

Put the other base on the TOP LEFT side of your table

5

STEP 3.

Put the base 10 number on the TOP RIGHT side of your table

574

STEP 4.

Divide the base 10 number by the other base

574

STEP 5.

Write your result under the base 10 number

574
14

STEP 6.

Write the remainder in front of your result

574
14 remainder » 4

STEP 7.

Repeat step — 4, 5, 6 for every result until your result is less than the other base

574
514 remainder » 4
2 remainder » 4

STEP 8.

Once your result is less than the other base, write ZERO as your next result

574
514 remainder » 4
52 remainder » 4
0

STEP 9.

Put your last result as the remainder

574
514 remainder » 4
52 remainder » 4
0 remainder » 2

STEP 10 — final answer

Write out the remainders from the BOTTOM to the TOP

= 244

FINAL ANSWER:

74 (in base ten)

= 244 (in base five)

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Click the button to practice questions on number base.

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