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Question

According to Euclid's division algorithm, HCF of any two positive integers a and b with a>b is obtained by applying Euclid's division lemma to a and b to find q and r such that a=bq+r, where r must satisfy
  1. 1<r<b
  2. 0<r<b
  3. 0r<b
  4. 0<rb

A
1<r<b
B
0<r<b
C
0r<b
D
0<rb
Solution
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According to Euclid's division algorithm, HCF of any two positive integers a and b with a>b is obtained by applying Euclid's division lemma to a and b to find q and r such that a=bq+r
The remainder r is either equal to or greater than 0 but it is always smaller than divisor b.
i.e 0r<b
Hence, option C is correct.

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