Question

$\text{Show that}527+752+275\text{is exactly divisible by 14.}$

Answer 1

Property:

$abc=100a+10b+c...\left(i\right)bca=100b+10c+a...\left(ii\right)andcab=100c+10a+b...\left(iii\right)\text{Adding, (i), (ii) and (iii), we get}abc+bca+cab=111a+111b+111c=111(a+b+c)=3\times 37(a+b+c)\text{Now, let us try this method on}527+752+275\text{to chck is it exactly divisible by 14}Here,a=5,b=2,c=7527+752+275=3\times 37(5+2+7)=3\times 37\times 14\text{Hence, it shos that}527+752+275\text{is exactly divisible by 14}$