Question

Find the H.C.F. of 180, 252 and 324 using Euclid’s Division Lemma.

Answer 1

First of all consider 252 and 324. here, a = 324

And b =252

By euclid's division lemma-

a = bq + r, 0 < or = r < b

324 = 252 * 1 + 72

252 = 72 * 3 + 36

72 = 36 * 2 + 0

Therefore, HCF (252, 324) = 36

Now consider 36 and 180. here a=180 and b=36.

By euclid's division lemma-  a = bq + r, 0 < or = r < b

180 = 36 * 5 + 0

Therefore, HCF ( 180, 36 ) = 36

Hence, HCF(180, 252, 324)

= 36

Answer 2

consider 252 and 324. here, a=324 and b=252

by euclid's division lemma-

a=bq+r, 0< or= r<b

324=252*1+72

252=72*3+36

72=36*2+0

therefore, HCF(252, 324)=36

Now consider 36 and 180. here a=180 and b=36.

by euclid's division lemma- a=bq+r, 0< or = r < b

180=36*5+0

therefore, HCF(180, 36)=36

Hence, HCF(180, 252, 324)=36