Prove that when abc is a multiple of 37,then so is the number bca Note: abc ,bca are numbers.

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Prove that when abc is a multiple of 37,then so is the number bca

Note: abc ,bca are numbers.

abc,bca are not product

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Ximena 1 month 2021-08-21T12:47:39+00:00 1 Answer 0 views 0

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    2021-08-21T12:48:48+00:00

    \textbf{Given:}

    \text{abc is a multiple of 37}

    \textbf{To prove:}

    \text{bca is a multiple of 37}

    \textbf{Solution:}

    \text{Since abc is a multiple of 37, we can write}

    abc=37\,k\;\;\text{where k is an integer}

    100\,a+10\,b+c=37\,k\;———–(1)

    \text{Now,}

    bca

    =100\,b+10\,c+a

    =10(10\,b+c)+a

    \text{Using (1), we get}

    =10(37\,k-100\,a)+a

    =370\,k-1000\,a+a

    =370\,k-999\,a

    =37(10\,k-27\,a)\;\;\text{which is a multiple of 37}

    \textbf{Hence proved}

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