Question

Use Euclid's division algorithm to find the HCF of the following: 1. 4052 and 12576.​

Answer 1

Answer:

refer to the attachment

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Answer 2

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According to Euclid’s Division Lemma if we have two positive integers a and b, then there exist unique integers q and r which satisfies the condition a = bq + r where 0 ≤ r ≤ b.

The HCF is the largest number that exactly divides two or more positive integers.

Since 12576 > 4052

12576 = (4052 × 3) + 420

420 is a reminder that is not equal to zero (420 ≠ 0).

4052 = (420 × 9) + 272

271 is a reminder that is not equal to zero (272 ≠ 0).

Now consider the new divisor 272 and the new remainder 148.

272 = (148 × 1) + 124

Now consider the new divisor 148 and the new remainder 124.

148 = (124 × 1) + 24

Now consider the new divisor 124 and the new remainder 24.

124 = (24 × 5) + 4

Now consider the new divisor 24 and the new remainder 4.

24 = (4 × 6) + 0

Reminder = 0

Divisor = 4

HCF of 12576 and 4052 = 4.