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Using Euclid’s division algorithm, the HCF of 8840 and 23120 is ____.

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Detailed Solution

Using Euclid’s division algorithm, the HCF of 8840 and 23120 is 680.
Given 2 numbers 8840 and 23120.
Applying Euclid’s division Lemma,
Assume a = 23120 and b =8840,

23120 = 8840 × 2 + 5440 H e r e, r = 5440 ≠ 0.

So, Dividend = 8840 and divisor = 5440.
Applying Euclid’s division Lemma,
Assume a = 8840 and b =5440,

8840 = 5440 × 1 + 3400 H e r e, r = 3400 ≠ 0

So, Dividend = 5440 and divisor = 3400.
Applying Euclid’s division Lemma,
Assume a = 5440 and b =3400,

5440 = 3400 × 1 + 2040 H e r e, r = 2040 ≠ 0.

So, Dividend = 3400 and divisor = 2040.
Applying Euclid’s division Lemma,
Assume a = 3400 and b =2040,

3400 = 2040 × 1 + 1360 H e r e, r = 1360 ≠ 0

So, Dividend = 2040 and divisor = 1360.
Applying Euclid’s division Lemma,
Assume a = 2040 and b =1360,

2040 = 1360 × 1 + 680 H e r e, r = 680 ≠ 0

So, Dividend = 1360 and divisor = 680.
Applying Euclid’s division Lemma,
Assume a = 1360 and b =680,

1360 = 680 × 2 + 0 H e r e, r = 0

Therefore, the value is 680.
Hence, the HCF of both numbers is 680.

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