
Calculate the remainder when \[30\] is divided by \[7\]?
Answer
411.6k+ views
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.
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.
Recently Updated Pages
What percentage of the area in India is covered by class 10 social science CBSE

The area of a 6m wide road outside a garden in all class 10 maths CBSE

What is the electric flux through a cube of side 1 class 10 physics CBSE

If one root of x2 x k 0 maybe the square of the other class 10 maths CBSE

The radius and height of a cylinder are in the ratio class 10 maths CBSE

An almirah is sold for 5400 Rs after allowing a discount class 10 maths CBSE

Trending doubts
For Frost what do fire and ice stand for Here are some class 10 english CBSE

What did the military generals do How did their attitude class 10 english CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

What did being free mean to Mandela as a boy and as class 10 english CBSE

Why is there a time difference of about 5 hours between class 10 social science CBSE

What did Valli find about the bus journey How did she class 10 english CBSE
