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Here I provide the image. My question is why is it necessary to have 2 different results of the same problem. Am I doing something wrong. Please Help!

enter image description here

Thanks in advance.

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In the first calculation, you are dividing $(432)_5$ by $3$. The result should not be $(144)_5$. What has been calculated is the base $3$ representation of $(432)_{10}$.

In the second calculation, where you are using the familiar base $10$ representation as intermediary, the calculations are right.

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