Question

Cube of even natural numbers is ____ number.
A.Even
B.Odd
C.Negative
D.Prime

Answer 1

Hint: In the above question, we can simply check if a cube of even natural numbers is even or not. We can check it by calculating cubes of even and odd natural numbers. We can calculate the cube by multiplying the given number three times; that is; $ {a^3} = a \times a \times a $ .

Complete step-by-step answer:
Multiplication of three even natural numbers will be always even. It means a cube of even natural numbers is an even number.
Let’s see few examples to prove this;
Cube of 12 = 12 $ \times $ 12 $ \times $ 12 = 1,728
Cube of 16 = 16 $ \times $ 16 $ \times $ 16 = 4,096
Here we can see that cube of 12 is 1,728 which is an even number and cube of 16 is 4,096 which is also an even number.
Cube of 13 = 13 $ \times $ 13 $ \times $ 13 = 2,197
Cube of 19 = 19 $ \times $ 19 $ \times $ 19 = 6,859
Here we can see that cube of 13 is 2,197 which is an odd number and cube of 19 is 6,859 which is also an odd number.
From the above examples we can say that the cube of an even number will always be an even number and the cube of an odd number will always be an odd number.
So, the correct answer is “Option A”.

Note: Natural numbers are a part of the number system which includes all the positive integers from 1 till infinity. It does not include zero. 1, 2, 3, 4, 5, 6, 7, 8, 9, …... are also called counting numbers.
Even numbers are integers that are exactly divisible by 2 or the number which ends with 2, 4, 6, 8, 0. Examples: 2, 6, 10, etc.