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Using Euclid’s division algorithm, the HCF of 4052 and 12576 is ____.

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Detailed Solution

Using Euclid’s division algorithm, the HCF of 4052 and 12576 is 4.
Given 2 numbers 4052 and 12576.
Applying Euclid’s division Lemma,
Assume a = 12576 and b =4052,

12576 = 4052 × 3 + 420 H e r e, r = 420 ≠ 0.

So, Dividend = 4052 and divisor = 420.
Applying Euclid’s division Lemma,
Assume a = 4052 and b =420,

4052 = 420 × 9 + 272 H e r e, r = 272 ≠ 0

So, Dividend = 420 and divisor = 272.
Applying Euclid’s division Lemma,
Assume a = 420 and b =272,

420 = 272 × 1 + 148 H e r e, r = 148 ≠ 0

So, Dividend = 272 and divisor = 148.
Applying Euclid’s division Lemma,
Assume a = 272 and b =148,

272 = 148 × 1 + 124 H e r e, r = 124 ≠ 0.

So, Dividend = 148 and divisor = 124.
Applying Euclid’s division Lemma,
Assume a = 148 and b =124,

148 = 124 × 1 + 24 H e r e, r = 24 ≠ 0

So, Dividend = 124 and divisor = 24.
Applying Euclid’s division Lemma,
Assume a = 124 and b = 24,

124 = 24 × 5 + 4.

H e r e, r = 4 ≠ 0

Applying Euclid’s division Lemma,
Assume a = 24 and b = 4,

24 = 4 × 6 + 0 H e r e, r = 0

Therefore, the value is 4.
Hence, the HCF both numbers is 4.

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