Euclid's division lemma states that for positive integers $a$ and $b$,…

Question

Euclid's division lemma states that for positive integers $a$ and $b$, there exist unique integers $q$ and $r$ such that

Accepted Answer

C. $a = bq + r,\ 0 \le r < b$

1. Dividing a by b gives a quotient q and a remainder r.
2. Euclid's lemma: $a = bq + r$ with $0 \le r < b$ (the remainder is always less than the divisor).
3. This is the basis of Euclid's algorithm for the HCF.
_Source: Karnataka SSLC (KSEEB) Class 10 Mathematics, Ch8 'Real Numbers', §8.2_

Answer

$a = bq + r,\ 0 < r \le b$

Answer

$b = aq + r,\ 0 \le r < a$

Answer

$a = bq - r,\ r > b$