Question

EXERCISE 1.1
(1. Use Euclid's division algorithm to find the HCF of-
(iii) 867 and 255
​

Answer 1

Given :

• 867 and 255

To find :

• HCF of 867 and 255 by Euclid's division algorithm =?

Step-by-step explanation:

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 ,

Start with a larger integer , that is 867,

Applying the Euclid's division lemma to 867 and 255, we get

867 = 255 x 3 + 102

Since the remainder 102 ≠ 0, we apply the Euclid's division lemma to divisor 255 and remainder 102 to get

255 = 102 x 2 + 51

We consider the new divisor 102 and remainder 51 and apply the division lemma to get

102 = 51 x 2 + 0

Now, the remainder at this stage is 0.

So, the divisor at this stage, i.e, 2 is the HCF of 867 and 255.

Answer 2

Answer:

As, 867=255 × 3 +102

255 = 102 × 2 + 51

102 = 51 × 2 + 0

So, HCF (867,255) = 51

Step-by-step explanation:

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