Correct Answer - Option 1 : 0
Concept:
Euclid's division lemma: If a and b are two positive integers, then there exists unique positive integers q and r such that
\(a=bq+r\) where \(0\leq{r}\ <\ {b}\) .
If b ∣ a then r = 0 otherwise r must satisfy stronger inequality 0 < r < b.
Calculation:
Let the required number be n.
According to the question, when n is divided by 3 it leaves 5 as the
remainder.
Therefore, by using Euclid’s division lemma, we will get
n = 3q + 5 where q is quotient
⇒ 3n = 3(3q+5)
⇒ 3n = 9q + 15
⇒ 3n + 3 = 9q + 18
⇒ 3n + 3 = 3 (3q + 6)
Hence, the remainder is 0.
- Euclid’s division algorithm is a technique to compute the Highest Common Factor (HCF) of two given positive integers.
- The HCF of two positive integers a and b is the largest positive integer d that divides both a and b.
