Question

find the hcf of the numbers using the division method 180,144,192 long division

Answer 1

By Euclid's Division Lemma

a = bq + r where 0 < r < b

For a = 180 b = 144

180 = 144 × 1 + 36 ( r # 0 )

For a = 144 b = 36

144 = 36 × 4 + 0 ( r = 0 )

Hence HCF [ 180 and 144 ] = 36

On applying

192 > 36

For a = 192 b = 36

192 = 36 × 5 + 156 ( r # 0 )

For a = 156 b = 36

156 = 36 × 4 + 120 ( r # 0 )

For a = 120 b = 36

120 = 36 × 3 + 84 ( r # 0 )

For a = 84 b = 36


84 = 36 × 2 + 48 ( r # 0 )

For a = 48 b = 36

48 = 36 × 1 + 12 ( r # 0 )

For a = 36 b = 12


36 = 12 × 3 + 0 ( r = 0 )


Therefore HCF [ 180, 144 and 192 ] = 12


Hope it helps!!