Question

FIND THE HCF USING EUCLID DIVISION LEMMA 1.) 88,121 AND 1331 2.) 38,78 AND 278 3.) 108 AND 45 4.) 40 AND 6

Answer 1

$\huge{\mathfrak{Question:-}}$

Find the HCF of the following using Euclid Division lemma.

$\huge{\mathfrak{Solution:-}}$

$\bf{1).\;88\;,\;121\;and\;1331}$

$\sf{a=bq+r\;\;\;\;\;(Euclid\;division\;lemma)}$

$\sf{121 = 88\times 1+33}$

$\sf{88 = 33\times 2+22}$

$\sf{33=22\times 1+11}$

$\sf{22=11\times 2+0}$

$\sf{HCF(121\;and\;88)= 11}$

$\sf{1331 = 11\times 120 + 11}$

$\sf{11 = 11\times 1+0}$

$\boxed{\sf{HCF(88,\;121\;and\;1331)= 11}}$

$\bf{2).\;38\;,\;78\;and\;278}$

$\sf{a=bq+r\;\;\;\;\;(Euclid\;division\;lemma)}$

$\sf{78 = 38\times 2+2}$

$\sf{38 = 2\times 19+0}$

$\sf{HCF(78\;and\;38)= 2}$

$\sf{278 = 2\times 139+0}$

$\boxed{\sf{HCF(38,\;78\;and\;278)= 2}}$

$\bf{3).\;108\;and\;45}$

$\sf{a=bq+r\;\;\;\;\;(Euclid\;division\;lemma)}$

$\sf{108 = 45\times 2 + 18}$

$\sf{45 = 18\times 2 + 9}$

$\sf{18 = 9\times 2+0}$

$\boxed{\sf{HCF(108\;and\;45)=9}}$

${\bf{4).\;40\;and\;6}}$

$\sf{a=bq+r\;\;\;\;\;(Euclid\;division\;lemma)}$

$\sf{40 = 6\times 6+4}$

$\sf{6 = 4\times 1+2}$

$\sf{4 = 2\times 2+0}$

$\boxed{\sf{HCF(40\;and\;6)=2}}$