# . Use Euclid algorithm to find the HCF of 4052 and 12576.

Step 1 : Since 12576 > 4052, we apply the pision lemma to 12576 and 4052, to get

12576 = 4052 × 3 + 420

Step 2 : Since the remainder 420   0, we apply the pision lemma to 4052 and 420, to get

4052 = 420 × 9 + 272

Step 3 : We consider the new pisor 420 and the new remainder 272, and apply the pision lemma to get

420 = 272 × 1 + 148

We consider the new pisor 272 and the new remainder 148, and apply the pision lemma to get

272 = 148 × 1 + 124

We consider the new pisor 148 and the new remainder 124, and apply the pision lemma to get

148 = 124 × 1 + 24

We consider the new pisor 124 and the new remainder 24, and apply the pision lemma to get

124 = 24 × 5 + 4

We consider the new pisor 24 and the new remainder 4, and apply the pision lemma to get

24 = 4 × 6 + 0

The remainder has now become zero, so our procedure stops. Since the pisor at this stage is 4, the HCF of 12576 and 4052 is 4.
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