Question

Use Euclid's division algorithm—
i) 135 and 225.
ii) 867 and 255​

Answer 1

Question :–

Use Euclid's division algorithm to find the HCF of :

i) 135 and 225

Solution:

Step 1 :- Since 225 is larger than 135, we apply the division lemma to 225 and 135, to get

225 = 135 × 1 + 90

Step 2 :- Since the remainder 90 is not equal to 0, we apply the division lemma to 135 and 90, to get 135 = 90 × 45

Step 3 :- We consider the new divisor 90 and the remainder 45, and apply the division lemma to get 90 = 45 × 2 + 0

The remainder has now became zero, so our procedure stops. Since the divisor at this stage is 45, the HCF of 135 and 225 is 45.

ii) 867 and 255

Solution :

( By the same mathod )

867 = 255 × 3 + 102

255 = 102 × 2 + 51

102 = 51 × 2 + 0

Hence, HCF of 867 and 255 is 51.

Answer 2

Explanation:

Use Euclid's division algorithm—

i) 135 and 225.

ii) 867 and 255

Refer to the attachment ..