Question

According to Euclid's Division Lemma a and b are any two integers with b is not equal to 0. then, there exists unique integers q and r such that a = bq + r, where 0 is less than or equal to r and r is less than | b |, but when we divide 8 by 3 we got the remainder and quotient 2 both are equal then how can Euclid's Division Lemma said that q and r are two unique integers ?​

Answer 1

Step-by-step 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 and r = Remainder.

Hence, the values 'r’ can take 0≤r<b.