Question

Every number is a ____ and ____ of itself.
A.Factor, multiple
B.Prime, composite.
C.Even, odd.
D.None of these.

Answer 1

Hint: Here, we will analyse all the given options and then we will recollect their definitions and see if the option fits in the blank. We will also check if the given option is appropriate to complete the sentence. We will use examples of the given terms and see if the numbers are satisfying the requirements of the question.

Complete step-by-step answer:
We will start analysing with option A.
A factor is any number that divides another number completely (gives a quotient that’s a whole number) and leaves a remainder of 0. Every number is a factor of itself because when any number is divided by itself, we obtain 1 as the quotient and 0 as the remainder.
Let us understand this with the help of an example; take any number say 12. 12 can be expressed in the following ways:-
\[\begin{array}{l}12 = 1 \times 12\\12 = 2 \times 6\\12 = 3 \times 4\end{array}\]
1, 2, 3, 4, 6 and 12 are the different factors of 12.
When any number is multiplied with an integer, the result obtained is called the multiple of that number. Every number is a multiple of itself because when a number is multiplied by 1, the same number is obtained. We can take the example of 12 again:-
\[12 \times 1 = 12\]
We can clearly see that 12 is a multiple of itself.
Now, let us see option B.
Any number that has only 2 factors, 1 and itself is called a prime number. Any number that is not a prime number is called a composite number. A number can’t be prime and composite at the same time. So option B is incorrect.
Let us have a look at option C.
Any number that’s divisible by 2 is called an even number. Any number that’s not divisible by 2 is called an odd number. A number can’t be even and odd at the same time. So option C is incorrect.
Finally, let’s have a look at option D which is none of these.
We can see that option A is an appropriate choice for filling the blanks in the sentence
So option D is not required.

Note: Examples of prime numbers are 2, 3, 5, 7, 11, etc. Examples of composite numbers are 4, 6, 8, 9, 10, etc.
Every even number leaves a remainder of 0 when they are divided by 2 and odd numbers leave a remainder of 1 when they are divided by 2. Some of the examples of even numbers are 2, 4, 6, 8, 10, etc and examples of odd numbers are 1, 3, 5, 7, 9, etc.