Question

Is \[109\] a prime number?

Answer 1

Hint: We use the concepts of prime numbers and definitions of prime numbers to solve this problem. We also use divisibility rules to solve this problem. We will look at some examples of prime numbers and also some examples of numbers which are not prime numbers.

Complete step by step solution:
A prime number is a natural number greater than 1, which is divisible only by 1 and the number itself.
So, in other words, numbers which have only two divisors have been called prime numbers.
Now, consider the number 109.
Out of the numbers below 109, there are no numbers which divide 109 exactly, except 1.
So, there are only two factors or divisors for the number 109, which are 1 and 109.
So, it has only two divisors.
Therefore, we can conclude that, \[109\] is a prime number.

Additional information:
All other numbers other than prime numbers are called composite numbers.
For example, take the natural number 2.
So, the number 2 is only divisible by two numbers which are 1 and 2. So, 2 is a prime number.
Take another example 5, which also has two divisors 1 and 5. So, 5 is also a prime number.
These are the few prime numbers:
\[2,3,5,7,11,13,17,19,23,29,31,......\]
Every composite number can be written as a product of prime numbers.
For example, take number 24, which is a composite number.
We can write 24 as, \[24 = 2 \times 2 \times 2 \times 3\].

Note:
The number 1 is neither a prime number nor a composite number. And the number 2 is the least prime number. If a number has an even number as its last digit, then it is divisible by 2. This is the divisibility rule of 2.
Also remember that two prime numbers with a difference 2, are called twin primes.
For example, \[(3,5)\] and \[(11,13)\]