Letters to communicate and words to count. Numbers are like essentials, and we have infinite. After getting knowledge on even numbers and odd numbers. Then we need to learn about prime numbers. So let us have a detailed discussion on what is a prime number and how to identify if the given number is prime or not. Is there any method to find out the prime number etc. that will go through once?

So, let’s see how to find prime numbers using the factorization method.

What is a Prime number?

A prime number is a number that is a positive integer and has only two factors. The prime numbers start from two. That is more than one. Zero or negative integers may not be considered prime numbers.

The two factors of a prime number are one and the number itself. If any other number becomes a factor, it is treated as either an even or odd number. Any number then is said to be a prime number.

How to find prime numbers? 

Though we have different methods to find the prime numbers, factorisation is one of the most efficient! It is a simple and common method to find out the prime number. It involves a few steps. They are –

• First, we need to find out the factors for a given number by checking all multiplication factors.
• Make a note of all the factors, then count the total number of factors obtained.
• If the total number of factors is greater than 2, that is 3 or more, it is not a prime number. It is a composite number.
• If the total number of factors is equal to 2, then it is a prime number.

These are the few simple steps involved in finding a prime number. To get a clear idea, let’s implement these steps by solving an example.

Illustration

Take the number 55.

Let us find out whether it is a prime number or not?

First, find out the factors of 55.

Factors of 55 are 1,5,11.

As the factors of 55 are more than 2, which is 3, we can say that 55 is a composite number but not a prime number.

Now,

Let’s take the example of 3.

The prime factorisation of 3 is 1 x 3.

Here, we got only two factors: 1 and the number itself.

Therefore, 3 is a prime number.

Another method to find prime number

Besides the prime factorization method, we have two simple formulas to find out if the given number is the prime or not. They are –

Using the first method:-  2 and 3 are two consecutive natural numbers. They are prime numbers also as they contain only 2 factors. Apart from these two numbers, we can use a formula to find out whether the number is prime or not. The formula is 6 n 1 (or) 6 n – 1. For instance,

• 6(1) – 1 = 5
• 6(2) – 1 = 11
• 6(3) – 1 = 17
• 6(1) + 1 = 7
• 6(2) + 1 = 13
• 6(3) + 1 = 19…..so on

Using the second method:- especially for greater numbers, we have another formula to find out whether it is prime or not. n2 n 41 is the formula for finding prime numbers. For instance,

• (1)2 + 1 + 41 = 43
• (2)2 + 2 + 41 = 47
• (3)2 + 3 + 41 = 53
• (4)2 + 2 + 41 =  59…..so on

The method used for large numbers:-  we can check if the large number is prime or not using a few simple steps. It is also a method that uses divisibility conditions. The steps involved in this method are as follows –

• First, check the unit’s place of a given number. If the unit consists of numbers like 0, 2, 4, 6, 8, then it is not a prime number. It is an even number.
• Now add all the digits in the given number. If the sum of the digits of a given number is divisible by 3, the given number is not a prime number.
• After taking the first two steps, let’s find out the square root of the given number.
• Take the prime numbers available below the square root and divide the given number with all those numbers.
• If the given number is divisible by any of the above numbers, it is not a prime number. If the given number is not visible by any numbers below the square root, it is a prime number.

These are the various methods and checkpoints to find out the given number, whether it is a prime or not. Let’s note the available prime numbers below 500 in table form.

List of prime numbers between 1 to 600-

	2	3	5	7	11	13	17	19	23
29	31	37	41	43	47	53	59	61	67
71	73	79	83	89	97	101	103	107	109
113	127	131	137	139	149	151	157	163	167
173	179	181	191	193	197	199	211	223	227
229	233	239	241	251	257	263	269	271	277
281	283	293	307	311	313	317	331	337	347
349	353	359	367	373	379	383	389	397	401
409	419	431	431	433	439	443	449	457	461
463	467	479	487	491	499	503	509	521	523
541	547	557	563	569	571	577	587	593	599

Conclusion

Hence the prime number is a positive integer greater than 1 and has only two factors, as we learnt that the factors are one and themselves. We also went through various methods to find out if the number is either prime or not. Understanding and finding prime numbers is just a cakewalk. It is simple but essential. These are like pillars of mathematics from which one can learn and move to an advanced level. To understand the concept and practice more examples to master the concept. 

Practice makes perfect!