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Thread: Dividing in Base 5, need help!!

  1. #1
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    Post Dividing in Base 5, need help!!

    The problem states, divide 538/ 14 in base 5. I already converted both numbers to base 5, 538= 4123 base 5, and 14= 24 base 5. I have started my division but feel like I am doing it wrong, as I keep getting 12311R3, and when using a conversion calculator online the answer comes out to 123. Can someone help me and explain what I'm doing wrong?
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  2. #2
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    Re: Dividing in Base 5, need help!!

    I do not see your work, which makes it difficult to help you. I would arrange it just like long division in base 10. 24 goes into 41 once (because 24*2 = 103 in base 5, which is bigger than 41). Next, 41-24 (in base 5) is 12. So, how many times does 24 go into 122? Well, 24*2 = 103 in base 5. If we add 24 again, it will be more than 122, so it is 2. Subtract again, and we get 14, and we carry down the 3. So, how many times does 24 go into 143? That would be 3 times. So, 24*3 = 132. Subtracting, we get a remainder of 11 (not a remainder of 3). So, the answer is 123R11. Let's convert back to base 10 to see how we did:

    123 converts to 38 in base 10. 11 converts to 6 in base 10. So, we expect our answer is 38R6 in base 10. Let's check:

    38*14 + 6 = 538 checks out. The correct answer is 38R6 in base 10 or 123R11 in base 5.
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