how to find by root method whether a no. is prime or not?
Answers
Step-by-step explanation:
Methods to Find Prime Numbers Easily
There are various methods to determine whether a number is prime or not. The best way for finding prime numbers is by factorisation method. By factorisation, the factors of a number are obtained and, thus, one can easily identify a prime number.
Finding Prime Numbers Using Factorization
Factorisation is the best way to find prime numbers. The steps involved in using the factorisation 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 more than two, 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 here 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 but a composite number.
Now, if we take the example of 19. The prime factorisation of 19 is 1 x 19. You can see here, there are two factors of 19. Hence, it is a prime number.
How to Tell if a Large Number is Prime?
There are some Prime Number Formulas, which can be used to find the primes. 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. If 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: Divide the given number by all the prime numbers below its square root value.
Step 5: 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.