Question

Find the hcf of 135 and 225using euclids divison algorithm

Answer 1

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Answer 2

Euclid's division lemma :

Let a and b be any two positive Integers .

Then there exist two unique whole numbers q and r such that

a = bq + r ,

0 ≤ r <b

Now ,

Clearly, 225 > 135

Start with a larger integer , that is 225.

Applying the Euclid's division lemma to 225 and 135, we get

225 = 135 x 1 + 90

Since the remainder 90 ≠ 0, we apply the Euclid's division lemma to divisor 135 and remainder 90 to get

135 = 90 x 1 + 45

We consider the new divisor 90 and remainder 45 and apply the division lemma to get

90 = 45 x 2 + 0

Now, the remainder at this stage is 0.

So, the divisor at this stage, ie, 45 is the HCF of 225 and 135.