What Are the Ways to Find Prime Numbers?

What Are the Ways to Find Prime Numbers?

by Manish Singh

Are you aware of how to locate prime numbers without difficulty? This article covers the notion of finding prime numbers (both large and small) using factorisation. When defining the term “prime number,” we know that prime numbers contain only two factors.

Two factors are 1.

Therefore, we must identify the numbers that comprise only two factors. The first factor and the initial number itself. This is achievable by using the most straightforward method, which is known as prime factorisation.

It is simple to locate some primes in small amounts; however, we must find another method to discover them for higher numbers. This is why we will explain how to calculate prime numbers, not just for smaller numbers but also for higher numbers.

In this article, students will discover a quick method to locate the prime number between 1 and 100 using the chart.

There are many fastest method to find Prime numbers. To find if a number has an exceptional value or not, then the most effective method to find prime numbers is through factorization. With factorization, factors of the number are derived and, this is how one can determine the prime number.

Finding Prime Numbers Using Factorisation

Factorization is the ideal method to locate prime numbers. The steps to follow when using the factorization technique are:

  • Step1: First, look up the components of the given number.
  • Step 2: Check the number of elements of that number.
  • Step 3: If you have a number greater than two, it’s not an integer prime.

Examples: Take a number, like 36.

The number 36 is described as (2 x 3) x 2. The factors of 36 are 2, 3, 4, 6, 9, 12, 18, and 36. Because the number of elements in 36 is more significant than, and it isn’t an integer, but rather a composite number.

Let’s take the case of 19. The primary number of factors in 19 would be 1x 19. As you can see, there are two elements of 19. This makes it an integer prime.

How to Tell if a Large Number is Prime?

There are a few Prime Number Formulas that are used to determine the prime numbers. To determine whether a massive amount of numbers is excellent or not, you must follow the instructions below:

  • Step 1: Check where the unit is located on the number if it ends with 0, 2, 4, 6, and 8.

Notice: “Numbers ending with 0, 2, 4, 6, and 8 are never prime numbers. ”

  • Step 2: Take the sum of this number. If the sum is divisible by 3, then this means that the number isn’t a prime number.

NOTE: “Numbers whose sum of digits are divisible by 3 are never prime numbers. ”

  • Step 3. After concluding that the number is not valid in grades 1, and 2 determine the square root for the number.
  • Step 4: Divide this number into all prime numbers in the square root.
  • Phase 5: If it is divided by one of the prime numbers but less than its square root. If it is, however, the number is considered to be exceptional.

Examples of finding Prime Numbers

Example 1:

  • You can take a number. For example, 234256.
  • The unit digit is 234256 is 6. It isn’t a prime number.

Example 2:

  • Choose a number, for example, 26577.
  • The unit of this number’s digit is not 0, 2, 4, 6, or 8.
  • Now, calculate the sum of the numbers that will be 2, 6, and 5 plus 7 = 27
  • Since 27 is divisible by three, 26577 isn’t a prime number.

Example 3:

  • You can also take another number, for example, 2345.
  • Because the number begins with 5, it can be divided by 5.
  • 2345/5 = 469.
  • So, aside from 2345 and 1, the number 5 also plays a role.
  • So, 2345 isn’t an ideal number.

Shortcut to Find Prime Numbers

One of the methods for finding the prime numbers is provided below.

  • Step 1: Write each number between 1 and 100 using six numbers in a row (as illustrated in the diagram).
  • Step 2: As 100’s square root is -10, you must eliminate the multiples of numbers until ten.
  • Step 3: Choose two and cross the entire column since all are multiples of 2. Also, it would be best to cross out all columns of 6 and 4 since they are both 2’s multiples.
  • Step 4: Now shift to step 3, then cross out the entire column.
  • Step 5: Take 5, and then cross diagonally toward the left. Then, you cross diagonally from the numbers 30, 60, 90, and 30. Then each of the five multiples has been crossed out.
  • Step 6: Choose 7, and then cross out diagonally to the right. Next, look for the following number in that column divided by seven and cross diagonally to the right. The first number on the column divisible to 7 is 49, and after that, the following number is 91—the diagonal crossing between 49 and 91 results in no more than 7 in the list.

The remaining numbers in the list of primes are also prime numbers. Below is a picture of the list.

Specific Important Points Concerning the Prime Numbers

  • “2” is the sole prime number that is even. All other primes are odd numbers.
  • “2” and “3” are the sole two prime numbers that are consecutive.
  • All even numbers that are more significant than two are represented as an equal sum of prime numbers.


In this article, we had studied the concepts of How to Find Prime Numbers in detail. I hope you understood the concept of what you are looking for. If you have any queries, please message us the details.


What’s the distinction between prime or composite numbers?

A prime number comprises only two elements, the number itself and one, whereas the composite number includes more than two elements. A prime number can be divided by just one, whereas the composite number is divided by all its features.

For instance, 2, 2 is a prime digit because it can be divided by 2 and 1 itself.

The number 9 can be described as a composite. It contains three factors, 1,3 and 9, and can be divided by all of its components.

Does one count as a prime or a composite number?

One isn’t a prime number nor an arithmetic number since one is divisible by itself, so it is only one factor. This is in contradiction to both definitions of a prime number as well as a composite number. Both contain more than two factors.

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