Question

The least two digit composite number is,
A. 11
B. 12
C. 10
D. 16

Answer 1

- Hint: We will be using the concept of prime and composite numbers to solve the problem. We will first find the least two digit number that is 10 then test it whether it is a composite number or not if it is composite then it will be the answer otherwise we will check the next number bigger than it for the composite number.

Complete step-by-step solution -

We have to find the least two digit number which is composite.
So, we know that a composite number is one which has more than two factors. For example, 4 has factors 1, 2 and 4. Therefore, 4 is a composite number.
Also, we should not a fact that any number is always divisible by 1 and the number itself. So, the least number of factors a number have is 2.
Now, we will first find the least two digit number. We know that the least two digit number is 10.
Now, we will test it whether the number is composite or not. So, we will find the factors of 10. So,
$10=1\times 2\times 5$
So, we can see that the factors of 10 are 1, 2, 5, 10 that is the factors of 10 are more than two or we can say that there exist a number except 10 and 1 which divides 10.
Therefore, 10 is composite and also 10 is the smallest two digit number.
Hence, option (C) is correct.

Note: To solve these types of questions students should know about composite numbers and their properties. It is important to note that we have used the fact that the lowest two digit number is 10 and we have checked it for composite numbers.