Question

use euclid's division algorithm to find whether the pair of numbers 615 and 154 is co prime or not

Answer 1

Answer:

$\red{ Given \: numbers \:615 \: and \: 154 \: are }$

$\green { Co-prime }$

Step-by-step explanation:

$\underline { \pink { Co-prime }}$

$If \: HCF \: of \: two \: numbers \: equal \: to \: 1 \\ then \: they \: are \: called \: Co-prime.$

$Given \: numbers \: 615 \: and \: 154$

$Here , 615 > 154$

$Start \: with \:the \: larger \:integer \: , that \:is, \\615. Apply \: the \: Euclid's \: division \: algorithm \\we \:get$

$615 = 154 \times 3 + 53$

$Since, \: the \: remainder \: 53 ≠ 0 , we \\apply \: the \: division \: algorithm \:to \: 53, to \:get$

$154 = 53 \times 2 + 48$

$53 = 48 \times 1 + 5$

$48 = 5 \times 9 + 3$

$5 = 3\times 1 + 2$

$3 = 2\times 1 + 1$

$2 = 1\times 2 + 0$

$The \: remainder \: has \: now \: become \\zero, \: so \: our \: procedure \: stops .$

$Since, the \: divisor \: at \:this \:stage \:is \: 1,\\HCF \: of \: 615\: and \: 154 \: is \: 1 .$

Therefore.,

$\red{ Given \: numbers \:615 \: and \: 154 \: are }$

$\green { Co-prime }$

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