Question

the largest number which divides 101 and 76 leaving remainders 3 and 6 respectively, is=?​

Answer 1

$Given \:two \:numbers \:101\:and \:76$

$\begin {tabular} { | c | c | c | }</p><p>\cline {1-3} number & remainder & new number\\</p><p>\cline {1-3} 101& 3&101-3 = 98 \\</p><p>\cline {1-3} 76 & 6 & 76 - 6 = 70 \\</p><p>\cline {1-3}</p><p> \end {tabular}$

$Now, \underline { Find \:the \:HCF \:of \:98\:and \:70: }$

$98 = 2 \times 7\times 7 \\70 = 2\times 5 \times 7$

$HCF (98,70) = 2\times 7 = 14$

Therefore.,

$The \:largest \:number \:which\: divides\: 101\\ and\: 76\: leaving\: remainders\: 3\: and\: 6\\ respectively, \:is \green {= 14 }$

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