Use Euclid's division algorithm to find the HCF of: (i) 135 and 225 (ii) 196 and 38220 (iii) 867 and 225

(i) 135 and 225
Step 1: First find which integer is larger. 225 > 135
Step 2: Then apply the Euclid's division algorithm to 225 and 135 to obtain 225 = 135 × 1 + 90
Repeat the above step until you will get remainder as zero.
Step 3: Now consider the divisor 135 and the remainder 90, and apply the division lemma to get 135 = 90 × 1 + 45
90 = 2 × 45 + 0
Since the remainder is zero, we cannot proceed further.
Step 4: Hence, the divisor at the last process is 45
So, the H.C.F. of 135 and 225 is 45
(ii) 196 and 38220
Step 1: First find which integer is larger. 38220 > 196
Step 2: Then apply the Euclid's division algorithm to 38220 and 196 to obtain 38220 = 196 × 195 + 0
Since the remainder is zero, we cannot proceed further.
Step 3: Hence, the divisor at the last process is 196.
So, the H.C.F. of 196 and 38220 is 196
(iii) 867 and 225
Step 1: First find which integer is larger. 867 > 255
Step 2: Then apply the Euclid's division algorithm to 867 and 255 to obtain 867 = 255 × 3 + 102
Repeat the above step until you will get remainder as zero.
Step 3: Now consider the divisor 225 and the remainder 102, and apply the division lemma to get 255 = 102 × 2 + 51
102 = 51 × 2 + 0
Since the remainder is zero, we cannot proceed further.
Step 4: Hence the divisor at the last process is 51.
So, the H.C.F. of 867 and 255 is 51.