Question

The number 222222 is.
(a) Divisible by 3 but not divisible by 7
(b) Divisible by 3 and 7 but not divisible by 11
(c) Divisible by 2 and 7 but not divisible by 11
(d) Divisible by 3,7 and 11

Answer 1

Hint: For solving this question we will directly divide the given number 222222 by 2, 3, 7 and 11 to check whether it is divisible by them or not.

Complete step-by-step answer:

Given:
We have to check the divisibility of number 222222 and answer whether it is divisible or not divisible by 2, 3, 7 and 11.
Now, first, we will divide the given number 222222 by 2, 3, 7 and 11 individually and then we will check whether 222222 is divisible by them or not.
Dividing the given number 222222 by 2:
\[2\overset{11111}{\overline{\left){\begin{align}
  & 222222 \\
 & \underline{2} \\
 & 022222 \\
 & \underline{02} \\
 & 002222 \\
 & \underline{002} \\
 & 000222 \\
 & \underline{0002} \\
 & 000022 \\
 & \underline{00002} \\
 & 000002 \\
 & \underline{000002} \\
 & \underline{000000} \\
\end{align}}\right.}}\]
Now, as the remainder is zero so, we conclude that 222222 is divisible by 2.

Dividing the given number 222222 by 3:
$3\overset{74074}{\overline{\left){\begin{align}
  & 222222 \\
 & \underline{21} \\
 & 012222 \\
 & \underline{012} \\
 & 000222 \\
 & \underline{00021} \\
 & 000012 \\
 & \underline{000012} \\
 & \underline{000000} \\
\end{align}}\right.}}$
Now, as the remainder is zero, we conclude that 222222 is divisible by 3.
Dividing the given number 222222 by 7:
$7\overset{31746}{\overline{\left){\begin{align}
  & 222222 \\
 & \underline{21} \\
 & 012222 \\
 & \underline{007} \\
 & 005222 \\
 & \underline{0049} \\
 & 000322 \\
 & \underline{00028} \\
 & 000042 \\
 & \underline{000042} \\
 & \underline{000000} \\
\end{align}}\right.}}$
Now, as the remainder is zero, we conclude that 222222 is divisible by 7.
Dividing the given number 222222 by 13:
$13\overset{17094}{\overline{\left){\begin{align}
  & 222222 \\
 & \underline{13} \\
 & 092222 \\
 & \underline{091} \\
 & 001222 \\
 & \underline{00117} \\
 & 000052 \\
 & \underline{000052} \\
 & \underline{000000} \\
\end{align}}\right.}}$
Now, as the remainder is zero, we conclude that 222222 is divisible by 13.
Thus, 222222 is divisible by 2, 3, 7 and 11.
Now, here the most suitable option will be (d).
Hence, (d) is the correct option.

Note: Here, for solving the option students should know how to divide any number by 2, 3, 7 and 11. Then, use it to find the correct option. While matching the options one should not get confused and select the most suitable option.