Is 65 a Prime Number?

Did you know 65 isn’t 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 65: 1,5,13 and 65.

• Number of divisors: 4

We can see that number 65 has four divisors. And we see that it doesn’t fulfill the criteria needed for a prime number. So it is not a prime number.
 

Let's check 65 is divisible by how many numbers. If 65 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 and 7. 

• That is, any number ending in an even number is divisible by 2. And 65 ends with an odd number. Actually, 5 is not a multiple of 2, so it is an odd number. So that 65 will not be divisible by 2 and it is not a prime number.

• The sum of the digits of the number 65 is 11. Now, in order to be divisible by 3, the sum of the digits needs to be a multiple of 3. Since 11 is not a multiple of 3. Therefore, 65 is not divisible by 3.

• 65 does end in 0 or 5. To be divisible by 5 a number should end in 0 or 5. So, 65 can be divided by 5.

• We know how to see whether 65 is divisible by 7. Let's simply glance at the last digit, which is 5. We have doubled that 5 to get 10, then subtract the other digit, which is 6. So, we do 10 – 6 = 4. Since 4 is not a multiple of 7, it means that 65 is not divisible by 7.

We see that 65 is exactly divisible by one of the above numbers. Hence, 65 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 65 does not appear here. So, it is not 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 65 is 13×5. Since there are more than two factors for 65, we can not call 65 a prime number.
 

• Composite number: a Composite number is a number having more than 2 factors. For example, : Also, 6 can be a composite number, 6 = 2 × 3.

• Test of divisibility: You find out how many numbers it divides into, and take down the number to which you want to do so. For example, 10. Of course this doesn’t though pass the divisibility test, as it can be divided by 1, and by 2 and by 5 and by 10.

• GCF: Greatest common factor is the highest factor that appears for a set of numbers. For all prime numbers, the GCF is 1.

• Natural number: It is basically the positive and whole numbers from 1.