Question

Use enclid division algorithm to find hcf of 240 and 6552

Answer 1

show the value of HCF is 24

Answer 2

$\underline { \pink { Euclid's \:Division \:Lemma :}}$

For Given positive integers a and b , there exist unique pair of integers q and r satisfying

$\boxed {\blue { a = bq + r }}$

Where, 0 ≤ r<b .

$Here, Given \:two \: positive \: numbers \:are \\240 \: and \: 6552$

$When \: 6552 \: is \: divided \:by \:240 \: the\\remainder \: is \: 72 , we \:get$

$6552 = 240 \times 27 + 72$

$Now, consider \: division \: of \: 240 \:with \\remainder \: 72 \: and \: apply \: the \: division \\lemma \: to \:get$

$240 = 72 \times 3 + 24$

$Again \: apply \: the \: division \:lemma$

$72 = 24 \times 3 + 0$

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

$Since, the \: divisor \: at \:this \:stage \: is \: 24\\the \: H.C.F \:of \: 6552 \: and \: 240 \:is \: 24$

Therefore.,

$\red { H.C.F \:of \: 6552 \: and \: 240}\green {= 24 }$

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