Is 127 a Prime Number?

Did you know 127 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 127: 1 and 127.

• Number of divisors: 2

We can see that number 127 has two divisors. And we see that it does fulfill the criteria needed for a prime number. So it is a prime number.
 

Let's check 127 is divisible by how many numbers. If 127 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 odd number is not divisible by 2. And 127 ends with an odd number. Actually, 7 is not a multiple of 2, so it is an odd number. So that 127 will not be divisible by 2 and it is not a prime number.

• The sum of the digits of the number 127 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, 127 is not divisible by 3.

• 127 does not end in 0 or 5. To be divisible by 5 a number should end in 0 or 5. So, 127 cannot be divided by 5.

• We know how to see whether 127 is divisible by 7. Let's simply glance at the last digit, which is 7. We have doubled that 7 to get 14, then subtract the other digit, which is 12. So, we do 14 – 12 = 2. Since 2 is not a multiple of 7, it means that 127 is not divisible by 7.

We see that 127 is not divisible by any of the above numbers. Hence, 127 is 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 127 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 127 is 127×1. Since there are only two factors for 127, we can call 127 a prime number.
 

• Composite number: The number which possesses more than 2 factor is named as composite number. Like, example- 18 is factorized into 2×32, thus it is a composite number.

• Factor: A number, if multiplied with another number, gives us the required number. Example, 7×2=14, 7×3=21. In that, 2 and 3 are factors.

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

• Co-prime Numbers: These numbers have a GCF of 1.