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.

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.

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.

Common Questions:

 Is 1 a Prime Number? Is 2 a Prime Number? Is 91 a Prime Number? Is 101 a Prime Number?

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.