. Using Euclids division algorithm find the HCF of 135 and 225

Best Answer

Explanation:

According to Euclid's division algorithm 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. That means, on dividing both the integers a and b the remainder is zero.

Given numbers are 135 and 225,

Here, 225>135

Applying Euclid’s division lemma to 225 and 135

225=135×1+90

Since the remainder is not equal to 0. So we apply the division lemma to the divisor 135 and remainder 90

⇒135=90×1+45

Apply the division lemma to the new divisor 90 and remainder 45

⇒90=45×2+0

Since the remainder is 0, the divisor will be the HCF(45).

Final Answer:

Hence, the HCF of 135 and 225 is 45.