Question

Check whether $ 6582 $ is divisible by $ 4 $ or not.

Answer 1

Hint: We will divide the given number with $ 4 $ and check if the remainder is Zero is not. If the remainder is zero, then we can write that the given number is divisible by $ 4 $. If the remainder is not equal to zero, then we can write that the given number is not divisible by $ 4 $.

Complete step by step answer:
Given number is $ 6582 $ .
     Dividing the given number $ 6582 $ with $ 4 $ as follows:
 $ 4\overline{\left){6582}\right.} $
First of all, we are going to divide 4 by 6 which we have shown below:
 $ 4\overset{1}{\overline{\left){\begin{align}
  & 6582 \\
 & \dfrac{4\downarrow }{25} \\
\end{align}}\right.}} $
In the above division, we have subtracted 4 from 6 and then carry the number 5 which is written after 6. Now, dividing 25 by 6 we get,
 $ 4\overset{14}{\overline{\left){\begin{align}
  & 6582 \\
 & \dfrac{4\downarrow }{\begin{align}
  & 25 \\
 & \dfrac{24}{18} \\
\end{align}} \\
\end{align}}\right.}} $
In the above division, we have subtracted 24 from 25 and then carried number 8. Now, we are going to divide 18 by 4.
\[4\overset{164}{\overline{\left){\begin{align}
  & 6582 \\
 & 4\downarrow \\
 & \overline{2}5 \\
 & 24 \\
 & \overline{01}8 \\
 & 016 \\
 & \overline{002} \\
\end{align}}\right.}}\]
On division of 18 by 4 we got 16 and then we subtracted 16 from 18. Then, we are going to carry the number 2 and write this number 2 after the result of subtraction of 16 from 18.
\[4\overset{164}{\overline{\left){\begin{align}
  & 6582 \\
 & 4\downarrow \\
 & \overline{2}5 \\
 & 24 \\
 & \overline{01}8 \\
 & 016 \\
 & \overline{002}2 \\
\end{align}}\right.}}\]
Now, dividing 22 by 4 we get,
\[4\overset{1645}{\overline{\left){\begin{align}
  & 6582 \\
 & 4\downarrow \\
 & \overline{2}5 \\
 & 24 \\
 & \overline{01}8 \\
 & 016 \\
 & \overline{002}2 \\
 & 0020 \\
 & \overline{0002} \\
\end{align}}\right.}}\]
From the above division, we have remainder as 2 when dividing 6582 by 4.
Here we got the remainder as $ 2 $ which is not equal to Zero.
 $ \therefore $ The given number $ 6582 $ is not divisible by $ 4 $ .

Note:
 We can also use the divisibility rule to check whether the number is divisible by $ 4 $ or not.
The divisibility rule for $ 4 $ is ‘If the last Two digits of the number are multiple of $ 4 $ , then the number is divisible by $ 4 $ ’. In the given number the last two digits are $ 82 $ which is not a multiple of $ 4 $ , so we can say that the given number $ 6582 $ is not divisible by $ 4 $ . Using the divisibility rule is the simple and fast method, so divisibility rules for other numbers are given below
For $ 2\to $ If the last digit in the given number is $ 2,4,6,8,0 $ .
For $ 3\to $ If the sum of the digits in the given number is multiple of $ 3 $ .
For $ 5\to $ If the last digit of the given number is $ 5 $ or $ 0 $.
For $ 6\to $ If the given number is divisible by $ 2 $ and $ 3 $ .
For $ 7\to $ If subtracting twice the last digit of the given number from the remaining digits gives a multiple of 7 (e.g. $ 658 $ is divisible by $ 7 $ because $ 65-2\times 8=49 $ , which is a multiple of $ 7 $ ).
For $ 8\to $ If the last three digits of the given number is multiple of $ 8 $ .
For $ 9\to $ If the sum of the digits of the given number is multiple of $ 9 $ .
For $ 10\to $ If the last digit of a given number is $ 0 $ .
For $ 11\to $ If the difference of the alternating sum of digits of given number is a multiple of $ 11 $ (e.g. $ 2343 $ is divisible by $ 11 $ because $ \left( 2+4 \right)-\left( 3+3 \right)=0 $ , which is a multiple of 11).