Question

hcf of 65and 100 by Euclid's division lemma

Answer 1

hcf is 5 for the question

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, 100 > 35

Start with a larger integer , that is 100.

Applying the Euclid's division lemma to 100 and 65, we get

100 = 65 × 1 + 35

Since the remainder 35 ≠ 0, we apply the Euclid's division lemma to divisor 65 and remainder 35 to get

65 = 35 × 1 + 30

We consider the new divisor 35 and remainder 30 and apply the division lemma to get

35 = 30 × 1 + 5

We consider the new divisor 30 and remainder 5 and apply the division lemma to get

30 = 5 × 6 + 0

Now, the remainder at this stage is 0.

So, the divisor at this stage, ie, 5 is the HCF of 100 and 65