Question

a natural number when dived by 15 gives a remainder 13.what will be the same natural number divided by 5​

Answer 1

$\large\text{\underline{Let's begin.}}$

$\hookrightarrow \text{Euclid's division lemma.}$

Let us consider the equation which is given by Euclid's division lemma,

$\implies A=BQ+R$

where,

• $A$ is the dividend
• $B$ is the divisor
• $Q$ is the quotient
• $R$ is the remainder

and there is a unique pair of integers $Q$ and $R$.

$\large\text{\underline{Solution}}$

Let's apply the division lemma here,

• $A$ is not given
• $B=15$
• $Q$ is not given
• $R=13$

So we get,

$\implies A=15Q+13$

If we try dividing by 5,

$\implies A=(15Q+10)+3$

$\implies A=5(3Q+2)+3$

Here, we can compare it to the division lemma. The quotient is $3Q+2$ and the remainder is $3$.

$\large\text{\underline{Conclusion}}$

Hence, the remainder is 3.

Answer 2

Solution :

$\sf \longrightarrow$ Given Natural number (N) when divided by 15 gives a reminder of 13.

$\sf \longrightarrow$ Let q be the quotient in that case.

$\sf \longrightarrow$ Hence,

• N = pq + r

• Where,
• N = Natural number
• p = divisor
• q = quotient
• r = reminder

Now, In Formula

• N = pq + r

• N = 15q + 13

• N = 15q + 10 + 3

• N = 5 ( 3q + 2 ) + 3

$\sf \longrightarrow$ Now when the Number N is divided by 5 it's going to gives remainder 3.

$\sf \longrightarrow$ as, 5 ( 3q + 2 ) is exactly divisible by 5.

I hope it helps you ❤️✔️