EXERCISE 1.1
(1. Use Euclid's division algorithm to find the HCF of-
(iii) 867 and 255
Answers
Answered by
8
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.
Answered by
9
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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