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Use Euclid’s division algorithm to find the HCF of :1)135 and 225 2)196 and 382203).867 and 255

1). 135 and 225
We have 225 > 135,

So, we apply the division lemma to 225 and 135 to obtain

225 = 135 × 1 + 90
Here remainder $$90 \ne 0$$, we apply the division lemma again to 135 and 90 to obtain
135 = 90 × 1 + 45

We consider the new divisor 90 and new remainder $$45 \ne 0$$, and apply the division lemma to obtain
90 = 2 × 45 + 0
Since the remainder is zero, the process stops.

The divisor at this stage is 45

Therefore, the HCF of 135 and 225 is 45.

2). 196 and 38220
We have 38220 > 196,

So, we apply the division lemma to 38220 and 196 to obtain
38220 = 196 × 195 + 0

Since the remainder is zero, the process stops.
The divisor at this stage is 196,

Therefore, HCF of 196 and 38220 is 196.

3). 867 and 255
We have 867 > 225,

So, we apply the division lemma to 867 and 255 to obtain
867 = 255 × 3 + 102
Here remainder $$102 \ne 0$$, we apply the division lemma again to 255 and 102 to obtain
255 = 102 × 2 + 51
Here remainder $$51 \ne 0$$, we apply the division lemma again to 102 and 51 to obtain
102 = 51 × 2 + 0

Since the remainder is zero, the process stops.
The divisor at this stage is 51

Therefore, the HCF of 867 and 255 is 51.