Is 361 a Prime Number?

Did you know 361 is a prime number? But why? Let us look at the rules a number has to follow to be a prime number to be a prime number.

• It should have only 2 factors: 1 and itself.

• It should have just 2 divisors.

In the rules which satisfy the 2 above, every number that comes next is of a prime number.

We could find that a number is prime if it has 2 factors only, 1 and the number itself. 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

Let's see how each of these tests helps us in finding prime numbers.
 

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.

• Divisors of 361: 1, 19 and 361.

• Number of divisors: 3

We can see that number 361 has three divisors. And we see that it does fulfill the criteria needed for a prime number. So it is a prime number.
 

Let's check 361 is divisible by how many numbers. If 361 is divisible by even one of the numbers, then it will not be a prime number. Let's check the divisibility with 2,3,5,7 and 19. 

• That is, any number ending in an odd number is not divisible by 2. And 361 ends with an odd number. Actually, 1 is not a multiple of 2, so it is an odd number. So that 361 will not be divisible by 2 and it is not a prime number.

• The sum of the digits of the number 361 is 10. Now, in order to be divisible by 3, the sum of the digits needs to be a multiple of 3. Since 10 is not a multiple of 3. Therefore, 361 is not divisible by 3.

• 361 does not end in 0 or 5. To be divisible by 5 a number should end in 0 or 5. So, 361 cannot be divided by 5.

• We know how to see whether 361 is divisible by 7. Let's simply glance at the last digit, which is 1. We have doubled that 1 to get 2, then subtract the other digit, which is 36. So, we do 36 – 2 = 34. Since 34 is not a multiple of 7, it means that 361 is not divisible by 7.

• Double the digit in one's place. It is 1 here and it becomes 2. So just add 2 to the rest of the number.(36+2=38)We get 38 as the sum. 361 is divisible by 19 because 38 is exactly divisible by 19.

We see that 361 is divisible by one of the above numbers. Hence, 361 is a prime number
 

Here, we will be using a chart that will contain all the prime numbers between 300 and 400. If the given number appears in the list, it is not a prime number. 
 

We can see that 361 does appear here. So, it is a prime number.
 

This method is used to break huge numbers into smaller numbers and find the prime factors of the given number. We know the prime factorization of 361 is 19×19. Since there are only two factors for 361, we can call 361 a prime number.
 

• Composite number: Now, the number with more than 2 factors is called the composite number. For example, 18 is factored as 2×32, so it’s a composite number.

• Co-prime Numbers: GCF of these numbers is 1.

• Factor: A factor is any number which when divided by other number gives the remaining number, which can not further be divided and is called factors. For example, 4/2=2. 2 is a divorce; it can divide 4 evenly.

• Natural number: 1 set of all the numbers which are positive and whole numbers.