Question

Find the hcf of 45,75 by euclids division lemma

Answer 1

Answer:

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The answer of your question is 15

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Answer 2

Answer:

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, 75 > 45

Start with a larger integer , that is 75.

Applying the Euclid's division lemma to 75 and 45, we get

75 = 45 × 1 + 30

Since the remainder 30 ≠ 0, we apply the Euclid's division lemma to divisor 45 and remainder 30 to get

45 = 30 × 1 + 15

We consider the new divisor 30 and remainder 15 and apply the division lemma to get

30 = 15 × 2 + 0

Now, the remainder at this stage is 0.

So, the divisor at this stage, ie, 15 is the HCF of 75 and 45.