Question

The least two digit composite number is
(a) 11 (b) 12 (c) 10 (d) 16

Answer 1

Hint:
Here, we need to find the least two digit composite number. We will use the divisibility rules to check which of the given options is a composite number or a prime number. Then, we will check which of the composite numbers is the smallest to find the least two digit composite number.

Complete step by step solution:
In the number system, prime numbers are the numbers which have only two factors, that is 1 and the number itself. Hence, it is obvious that they will be divisible by 1 and the number itself.
Composite numbers are the numbers which are not prime numbers. They are divisible by factors other than 1 and themselves.
We will check the given options to find which of the given options is a composite number.
The first number is 11.
We know that 11 is not divisible by any number other than 1 and itself.
Therefore, 11 is a prime number.
Thus, option (a) is incorrect.
The next number is 12.
We will check the divisibility by 2.
We know that all even numbers are always divisible by 2.
Hence, the number 12 is divisible by 2.
Since 12 is divisible by a number other than itself, it is a composite number.
The next number is 10.
We will check the divisibility by 2.
We know that all even numbers are always divisible by 2.
Hence, the number 10 is divisible by 2.
Since 10 is divisible by a number other than itself, it is a composite number.
The next number is 16.
We will check the divisibility by 2.
We know that all even numbers are always divisible by 2.
Hence, the number 16 is divisible by 2.
Since 16 is divisible by a number other than itself, it is a composite number.
Thus, 10, 12, 16 are the composite numbers.
We can observe that 10 is the least composite number compared to 12 and 16.
Also, we know that the smallest two digit number is 10.
Therefore, we can conclude that there is no two digit composite number smaller than 10.
Hence, 10 is the least two digit composite number.

Thus, the correct option is option (c).

Note:
We used the divisibility rule that all even numbers are divisible by 2. This means that every number that has 2, 4, 6, 8, or 0 in the unit’s place is divisible by 2, and is thus, a composite number.
We can also solve the problem by listing the first few two digit numbers, for example 10, 11, 12, 13, 14, etc, and checking which of them is a composite number. Here, 10, 12, 14 are composite numbers, and 10 is the least two digit composite number.