How to Find Prime Numbers?

Do you know how to find prime numbers? This article covers the concept of finding prime numbers (both small and large) easily using factorization. Here, students will also learn a shortcut way to find prime numbers from 1 to 100 using its chart.

How To Find Prime Numbers?

There are various ways to determine whether a number is prime or not. The best way for finding prime numbers is by factorization method. By factorization, the factors of a number are obtained and, thus, one can easily identify a prime number.

Finding Prime Numbers Using Factorization

Factorization is the best way to find prime numbers. The steps involved in using the factorization method are:

  • Step 1: First find the factors of the given number
  • Step 2: Check the number of factors of that number
  • Step 3: If the number of factors is greater than 2, it is not a prime number.

Example: Take a number, say, 36.

Now, 36 can be written as 2 × 3 × 2 × 3. So, the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. Since the number of factors of 36 is more than 2, it is not a prime number.

Also Check: Prime Factorization

How to Tell if a Large Number is Prime?

To check whether a large number is a prime number or not, follow the steps given below:

  • Step 1: Check the units place of that number. If it ends with 0, 2, 4, 6 and 8, it is not a prime number.

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

  • Step 2: Take the sum of the digits of that number. It the sum is divisible by 3, the number is not a prime number.

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

  • Step 3: After confirming the falsity of steps 1 and 2, find the square root of the given number.
  • Step 4: If the obtained number is a perfect square, retake its square root again.
  • Step 5: Divide the given number by all the prime numbers below its square root.
  • Step 6: If the number is divisible by any of the prime numbers less than its square root, it is not a prime number; otherwise, it is prime.

Try This: Prime Numbers Calculator

Example 1:

  • Take a number, say, 234256
  • Since the units digit of 234256 is 6, it is not a prime number.

Example 2:

  • Take a number, say, 26577
  • The units digit of this number is not 0, 2, 4, 6 or 8
  • Now, take the sum of digits which will be: 2 + 6 + 5 + 7 + 7 = 27
  • Since 27 is divisible by 3, 26577 is not a prime number.

Example 3:

  • Take another number, say, 2345
  • For this number, step 1 and step 2 does not hold true
  • So, take the square root of 2345, i.e. √2345 = 48.42
  • Now, start dividing 2345 with all the prime number below 48.42
  • It can be seen that the number 2345 is divisible by 5.
  • Hence, 2345 is also not a prime number.

How to Find a Prime Number Formula: Prime Number Formula

Common Questions:

Shortcut: How to Find Prime Numbers from 1 to 100?

One of the shortcuts to finding the prime numbers are given below.

  • Step 1: Write all the numbers from 1 to 100 with 6 numbers in a row (as shown in the figure).
  • Step 2: As the square root of 100 is 10, the multiples of numbers till 10 has to be crossed out.
  • Step 3: Choose 2 and cross the entire column as all are multiple of 2. Also, cross out the entire columns of 4 and 6 as those are also 2’s multiples.
  • Step 4: Now move to 3 and cross out the entire column.
  • Step 5: Take 5 and cross out the diagonally towards left. Then, cross out diagonally from numbers 30, 60, and 90. Now, all the multiples of 5 are crossed out.
  • Step 7: Choose 7 and cross out diagonally towards the right. Then, check the next number on that column which is divisible by 7 and cross diagonally right. The first number on that column that is divisible by 7 is 49 and then 91. Crossing diagonally right from 49 and 91 leaves no multiples of 7 on the list.

Now, the remaining numbers on this list are prime numbers. The image below shows this list.

How to Find Prime Numbers from 1 to 100

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