Using Euclid’s division algorithm, the HCF of 135 and 225 is ____.

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Detailed Solution

Using Euclid’s division algorithm, the HCF of 135 and 225 is 45.
Given 2 numbers 135 and 225.
Applying Euclid’s division Lemma,
Assume a = 225 and b =135,

225 = 135 × 1 + 90 H e r e, r = 90 ≠ 0.

So, dividend = 135 and divisor = 90.
Applying Euclid’s division Lemma,
Assume a = 135 and b =90,

135 = 90 × 1 + 45 H e r e, r = 45 ≠ 0

So, dividend = 90 and divisor = 45.
Applying Euclid’s division Lemma,
Assume a = 90 and b =45,

90 = 45 × 2 + 0 H e r e, r = 0

Therefore, the value is 45.
Hence, the HCF of both numbers is 45.

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