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Use euclid's algorithm to find HCF of 1651 and 2032 Express the HCF in the form of 1651 M + 2032 n​

Answer»

\huge\mathbb{\underline{SOLUTION:-}}

USE EUCLID division lemma to FIND the The H.C.F

\sf\implies {\blue{H.C.F\:of\:1651\:\:and\:\:2032}}\\ \\ \sf\implies 2032=1651\times 1+381\\ \\ \sf\implies 1651= 381\times 4+127\\ \\ \sf\implies 381=127\times 3+0\\ \\ \sf\:\:\:H.C.F =127

\sf \:\:127=1651-(127\times 4)\\ \\ \sf\:\:127=1651-[2032-(1651\times 1)]4\\ \\ \sf\:\:127= 1651-2032(4)+1651(4)\\ \\ \sf\:\:127=1651+1651\times 4 -2031(4)\\ \\ \sf\:\: 127=1651(1+4)-2032(4)\\ \\ \sf\:\: 127= 1651(5)+2032(-4)\\ \\ \sf\:\:127=1651m+2032n\\ \\ \sf\:\:so\:the\:value\:of\:m\:and\:n \:is\\ \\ \sf\:\: 5\:and\:(-4)

\boxed{\sf{\purple{VaLue\:of\:m\:and\:n= 5\:and\:(-4)}}}

Now \boxed{\sf{Verification:-}}

\sf \implies 1651\times (5)=8255\\ \\ \sf\implies 2032\times (-4) =(-8128)\\ \\ \sf\:\:Their\: Difference\:will\:be\:our\:H.C.F\\ \\ \sf\implies 8255-8128\\ \\ \sf\implies 127\:\:\:(Hence\: Verified)


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