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Using Euclid’s division algorithm, the HCF of 250, 175 and 425 is ____.

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Detailed Solution

Using Euclid’s division algorithm, the HCF of 250, 175 and 425 is 25.
Given 3 numbers 250, 175 and 425.
Applying Euclid’s division Lemma,
Assume a = 425 and b = 250,

425 = 250 × 1 + 175 H e r e, r = 175 ≠ 0.

So, Dividend = 250 and divisor = 175.
Applying Euclid’s division Lemma,
Assume a = 250 and b = 175,

175 = 75 × 2 + 25 H e r e, r = 25 ≠ 0.

So, Dividend = 75 and divisor = 25.
Applying Euclid’s division Lemma,
Assume a = 75 and b = 25,

75 = 25 × 3 + 0 H e r e, r = 0

Now, as remainder is 0.
H.C.F of 425 and 225 is 25.
Applying Euclid’s division Lemma,
Assume a =175 and b = 25,

175 = 25 × 7 + 0 H e r e, r = 0

The final value is 25.
Therefore, the HCF of 250, 175 and 425 is 25.

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