Question

Use euclids division algorithm to find the HCF of:

135 and 225
196 and 38220
867 and 255

Answer 1

Answer :

(i) 135 and 225
Since 225 > 135, we apply the division lemma to 225 and 135 to obtain
225 = 135 × 1 + 90
Since remainder 90 ≠ 0, we apply the division lemma to 135 and 90 to
obtain
135 = 90 × 1 + 45
We consider the new divisor 90 and new remainder 45, and apply the
division lemma to obtain
90 = 2 × 45 + 0
Since the remainder is zero, the process stops.
Since the divisor at this stage is 45,
Therefore, the HCF of 135 and 225 is 45.

(ii) 196 and 38220
Since 38220 > 196, we apply the division lemma to 38220 and 196 to
obtain
38220 = 196 × 195 + 0
Since the remainder is zero, the process stops.
Since the divisor at this stage is 196,
Therefore, HCF of 196 and 38220 is 196.

(iii) 867 and 255
Since 867 > 255, we apply the division lemma to 867 and 255 to obtain
867 = 255 × 3 + 102
Since remainder 102 ≠ 0, we apply the division lemma to 255 and 102
to obtain255 = 102 × 2 + 51
We consider the new divisor 102 and new remainder 51, and apply the
division lemma to obtain
102 = 51 × 2 + 0
Since the remainder is zero, the process stops.
Since the divisor at this stage is 51, Therefore,
HCF of 867 and 255 is 51.

Answer 2

1).
225>135
225=135×1+90
135=90×1+45
45=2×45+0
hence the HCF of 135&225 is 45
2).38220>196
38220=196×19+0
hence the HCF of 38220&196 is 19.

3).
867>225
867=225×3+102
225=102×2+51
102=51×2+0
hence the HCF of 867&255 is 51.