Is 21 a Prime Number?

21 is not a prime number. But according to what we are saying, why is it not a prime number? Let's understand that, firstly, the number set is of two parts:

• Prime number

• composite numbers

And using one of the methods we're going to introduce you to, we will find that indeed 21 is not a prime.

We could find that a number is prime if it has 2 factors only, 1 and the number itself, and only 2 divisors. It means that a number, not satisfying these conditions, cannot be a prime number.

However, there are pretty simple methods to determine whether a number is prime or not:

• Count Divisor Method

• Divisibility Test

• Prime Number Table

• Prime Factorization
   

The name implies: We’re counting how many divisors a given number has, and then saying that number is prime. It is easy to learn. With that said, let’s see what steps are there in this method.

• First is to count how many the number holds in divisors.

• We can then see that 21 has more than 2 divisors: 1,3,7 and 21.

We can see that number 21 has 4 divisors. Thus, we see that it doesn’t fulfill the criteria needed for a prime number. And so it is not a prime number.
 

In this case, we'll see if 21 can be divided into any other number. Now if it gets divided then that is not a prime number. So let’s check for 2,3,5 and 7.

• Since 21 is an even number, we can say that 21 is divisible by 2.

• Since the sum of the digits is 3, 3 is divisible by 3 as 3 is a multiple of 3. Hence, it is divisible by 3.

• 21 is not ending with a 0 or 5. Therefore, it is not divisible by 5.

• To see if 21 is divisible by 7, we can use a simple trick. First, we look at the last digit, which is 1. We double that 1 (1 × 2 = 2) and then subtract it from the other digit, which is 1. So, we do 2–2 = 0. 0 is not a multiple of 7,but when the difference is 0, the number will be divisible by 7. Hence, 21 is divisible by 7.

We know 21 can be divided by two of the above-mentioned numbers, therefore it is not a prime number.
 

Here, we will be using a chart that will contain all the prime numbers between 1 and 100. If the given number appears in the list, it is not a prime number. 
 

We can see that 21 does not appear here. So, it is not a prime number.
 

We use this method of breaking large numbers into small numbers, then checking the factors. It works only for composite numbers. 

The factors of 21 are 3 and 7. Since there are more than two factors for 21, we can not title 21 a prime number.
 

• Composite number- The number which possesses more than 2 factors is named as composite number. Like, example -  10 is factored into 2×5, thus it is a composite number. 

• Factor- A number that divides another number exactly is called a factor. For example, 10/5=2. Here, 5 is a factor.

• Prime Number Chart- A list of prime numbers, often used to quickly determine if a number is prime by checking if it appears in the list.

• Natural number All the numbers that are positive and whole numbers form 1.