In Euclid's division Lemma for positive integers $a$ and $b$ , the unique integers $q$ and $r$ are obtained such that $a = b q + r$ is

0 < r < b

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0 \leq r \leq b

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0 < r \leq b

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0 \leq r < b

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Solution

The correct option is C $0 \leq r < b$
According to Euclid's division lemma, for any given $a$ and $b$ , there exist unique non-negative integers $q$ and $r$ such that $a = b q + r, 0 \leq r < b$
Thus, the answer is $0 \leq r < b$

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Similar questions

According to Euclid's division lemma, if $a$ and $b$ are two positive integers with $a > b,$ then which of the following is true? (Here, $q$ and $r$ are unique integers.)

Q. Euclid's division lemma states that for two positive integers a and b , there exist unique integers q and r such that a = bq + r , where r must satisfy
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Q. Euclid's division algorithm states that for any positive integers a and b, there exist unique integers q and r such that

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In Euclid's division Lemma for positive integers a and b, the unique integers q and r are obtained such that a=bq+r is

The correct option is C 0≤r<bAccording to Euclid's division lemma, for any given a and b, there exist unique non-negative integers q and r such that a=bq+r, 0≤r<bThus, the answer is 0≤r<b

In Euclid's division Lemma for positive integers $a$ and $b$ , the unique integers $q$ and $r$ are obtained such that $a = b q + r$ is

The correct option is C $0 \leq r < b$
According to Euclid's division lemma, for any given $a$ and $b$ , there exist unique non-negative integers $q$ and $r$ such that $a = b q + r, 0 \leq r < b$
Thus, the answer is $0 \leq r < b$