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 74

_{10}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

5 | 74 |

## STEP 4.

### Divide the base 10 number by the other base

5 | |

## STEP 5.

### Write your result under the base 10 number

5 | |

14 |

## STEP 6.

### Write the remainder in front of your result

5 | |

14 remainder » 4 |

## STEP 7.

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

5 | |

5 | |

2 remainder » 4 |

## STEP 8.

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

5 | 74 |

5 | |

5 | remainder » 4 |

0 |

## STEP 9.

### Put your last result as the remainder

5 | 74 |

5 | |

5 | 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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