Question

find the HCF of 195, 416 by using euclid's division algorithm​

Answer 1

Answer:

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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, 416 > 195

Start with a larger integer , that is 416.

Applying the Euclid's division lemma to 416 and 195, we get

416 = 195 × 2 + 26

Since the remainder 26 ≠ 0, we apply the Euclid's division lemma to divisor 195 and remainder 26 to get

195 = 26 × 7 + 13

We consider the new divisor 26 and remainder 13 and apply the division lemma to get

26 = 13 × 2 + 0

Now, the remainder at this stage is 0.

So, the divisor at this stage, ie, 13 is the HCF of 416 and 195.