Question

According to Euclid's division lemma,for positive integer a and 7 if a=7q+r is unique then r=____________ is not possible

Answer 1

Step-by-step explanation:

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Answer 2

Given :- According to Euclid's division lemma,for positive integer a and 7 if a=7q+r is unique then r is ___________ ?

A) 0< r ≤ 7

B) 0 ≤ r < 7

C) 1 ≤ r ≤ 7

D) r ≥ 7 .

Answer :- B) 0 ≤ r < 7 .

Explanation :-

Euclid’s division Lemma:-

• It tells us about the divisibility of integers.
• It states that any positive integer a can be divided by any other positive integer b in such a way that it leaves a remainder r .

Euclid's division Lemma states that for any two positive integers a and b there exist two unique whole numbers q and r such that :-

• a = bq + r, where 0 ≤ r < b.

Here,

• a = Dividend.
• b = Divisor.
• q = Quotient.
• r = Remainder.

Hence,

• The values r can take = 0 ≤ r < b.

According to question now, we have ,a and 7 are positive integers , q is quotient and r is remainder .

Than,

• a = 7q + r

comparing a = 7q + r with a = bq + r , we get,

• b = 7 .

Therefore,

• The values r can take = 0 ≤ r < b
• => 0 ≤ r < 7.
• => Option (B) .

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