Is 217 a Prime Number?

The number 217 is indeed not considered as a prime number because it has more than two divisors, excluding the number one and itself. it has other factors.

A number is said to be a prime or not a prime only when certain conditions are met. To find those there are methods to perform and when the conditions are met only the numbers are categorized as prime and composite numbers.

The methods to check any numbers are as follows:

• Count Divisor Method

• Divisibility Test

• Prime Number Table

• Prime Factorization
   

Counting divisors method refers to a type of method where we count the number of divisors of a particular number to find out whether the number is a prime number or not.

If we look at 217 we can see that it has more than 2 divisors which are 1, 7, 13 and 217 . Since 217 has more than 2 divisors, it is not a prime number.
 

In this test, we try to find out the prime numbers that divide the number without leaving any reminder.

Hence, we can see that there are no prime numbers that are able to easily divide 217 without leaving any remainder.

Hence, this proves that 217 is not a prime number.

This is a rather simple method where we write down all the prime numbers until we cross the required number,

for example let's write down all the prime numbers from 1 to 230. 2, 3, 5, 7…. 199, 211, 223, 227.

From looking at the above list, we can see that 217 is not a prime number.
 

Prime factorization is a method where we represent a composite  number based on the factors of  two prime numbers.

In this case, the prime factors of the number 217 are 7 and 31, hence it is not a prime number.

• Prime Number Chart: A compilation of all the prime numbers till a certain given value.

• Divisor: An integer that evenly divides the number without any remainders.

• Prime Factorization: Multiplying two prime numbers to get one number is called prime factorization.