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# Calculate the remainder when $30$ is divided by $7$? Verified
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Hint: In order to find the remainder when $30$ is divided by $7$, we can either perform the process of division or apply the Euclid’s division algorithm and solve it by considering the remainder as a variable and the quotient as a nearer number that $7$ divides. The value of the variable will be our required answer.

Complete step-by-step solution:
Now let us briefly talk about the Euclid division algorithm. It is also called as Euclid division Lemma which states that $a,b$ are positive integers, then there exists unique integers satisfying $q,r$ satisfying $a=bq+r$ where $0\le r< b$.
Now let us find the remainder when $30$ is divided by $7$.
We know that the Euclid division algorithm is $a=bq+r$.
Here, we have $a=30,b=7$.
In order to find $q$, let us check such a number that divides $30$ or nearly divides it.
So we can observe such number as $28=7\times 4$
We get the value of $q$ as $4$.
Upon substituting, we obtain
\begin{align} & \Rightarrow a=bq+r \\ & \Rightarrow 30=7\left( 4 \right)+r \\ & \Rightarrow 30=28+r \\ & \Rightarrow 30-28=r \\ & \Rightarrow r=2 \\ \end{align}
$\therefore$ The remainder when $30$ is divided by $7$is $2$.

Note: We can also find the remainder by applying the division method as shown below.
$\dfrac{30}{7}=4$
Even in this case, we obtain the remainder as $2$.
Using the Euclid division algorithm we can also find the HCF of the numbers. We must have a point to note that the numbers must be positive in order to apply the Euclid division algorithm in order to obtain a unique quotient and remainder.