Question

State whether the following statement is true or false.
If an even number is divided by 2, the quotient is always odd.

Answer 1

Hint: Take up even numbers from the set of even numbers going from 2, 4, 6, 8………………. And divide it with two, any quotient that is the answer of this division comes out to be an even number then it is a false statement else true.

Complete step-by-step answer:
As we know, even numbers are those which are divisible by 2.
Therefore the set of even (E) numbers are
$E = \left( {2,4,6,8,10,12,14,............} \right)$
Now as we know that the quotient is the number how many times the number is divisible by the divisor.
In the question the divisor is 2.
We have to find out whether the quotient is always odd.
So divide even numbers with 2.
So divide first even number we have,
$\left( i \right)$ = $\dfrac{2}{2} = 1$
So as we know 1 is an odd number so the quotient is an odd number.
Now divide second even number we have,
$\left( {ii} \right) = \dfrac{4}{2} = 2$
So as we see that the quotient is 2 which is again an even number.
So we can say that when an even number is divided by 2 the quotient is sometimes odd sometimes even it is not always odd.
So the given statement is false.

Note: Numbers are said to be even which are exactly divisible by 2. The trick to find even numbers is that an even number will always end up with 0, 2, 4, 6 or 8. Even numbers can be written in a general manner as 2n where n belongs to the set of natural numbers from (1, 2, 3, 4………………………….).