Question

find the largest number which divides 1280 and 1371 leaving a remainder 6 in each case​

Answer 1

$\textbf{Given:}$

$\text{Numbers: 1280 and 1371}$

$\textbf{To find:}$

$\text{The largest no. which divides 1280 and 1371 leaving a remainder 6}$

$\textbf{Solution:}$

$\text{It is enough to find the largest no. which divides 1274 and 1365 exactly}$

$\text{That is, to find H.C.F of 1274 and 1365}$

$\begin{array}{r|l}2&1274\\\cline{2-2}7&637\\\cline{2-2}7&91\\\cline{2-2}13&13\\\cline{2-2}&1\\\cline{2-2}\end{array}$

$\begin{array}{r|l}3&1365\\\cline{2-2}5&455\\\cline{2-2}7&91\\\cline{2-2}13&13\\\cline{2-2}&1\\\cline{2-2}\end{array}$

$\text{From the above division, we get}$

$1274=2{\times}7{\times}\boxed{7{\times}13}$

$1365=3{\times}5{\times}\boxed{7{\times}13}$

$\text{H.C.F=}7{\times}13$

$\text{H.C.F=}91$

$\therefore\textbf{The largest no. which divides 1280 and}$

$\textbf{1371 leaving a remainder 6 is 91}$

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