Question

By Euclid division lemma find hcf of 156and196

Answer 1

Step-by-step explanation:

By Euclids division lemma , HCF (156, 196)

here, largest number is 196.

so, 196 = 156 × 1 + 40

156 = 40 × 3 + 36

40. = 36 × 1 + 4

36. = 4 × 9 + 0

Hence , here divisor is 4

Therefore , HCF of ( 156, 196). is 4.

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, 196 > 156

Start with a larger integer , that is 196.

Applying the Euclid's division lemma to 196 and 156, we get

196 = 156 × 1 + 40

Since the remainder 40 ≠ 0, we apply the Euclid's division lemma to divisor 156 and remainder 40 to get

156 = 40 × 3 + 36

We consider the new divisor 40 and remainder 36 and apply the division lemma to get

40 = 36 × 1 + 4

We consider the new divisor 36 and remainder 4 and apply the division lemma to get

36 = 4 × 9 + 0

Now, the remainder at this stage is 0.

So, the divisor at this stage, i.e., 4 is the HCF of 196 and 156.