Question

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


Help me

Answer 1

$\textbf{Given:}$

$\text{abc is a multiple of 37}$

$\textbf{To prove:}$

$\text{bca is a multiple of 37}$

$\textbf{Solution:}$

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

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

$100\,a+10\,b+c=37\,k\;$-----------(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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