Question

check whether following numbers are prime or composite 2×3+5

Answer 1

either 1 and number itself or more than two factors.
There are numbers who have exactly two factors – 1 and the number itself. These numbers are known as Prime Numbers. These numbers are 2, 3, 5, 7, 11 etc. 
There are other numbers which have more than two factors. These numbers are known as composite numbers. These numbers are 4, 6, 8, 9, 10, and 20 and so on. 
1 is neither a prime nor a composite number. 
In order to find whether a number is a prime number or a composite number, we need to factorize the given number. 
Solved example:- 
Check if 48 is a composite number or a prime number. 
48 
= 12 x 4 
= 3 x 4 x 4 
= 3 x 2 x 2 x 2 x 2 
48 has more than two factors. 
Hence, we can see that 48 is a composite number as it has more than two factors. 
If we do not want to factorize each and every number in order to see whether it is a prime number or a composite number, we can find the prime numbers from 1 to 100 with an easier method. 
Step 1: cross out 1 as it is not a prime number. 
Step 2: encircle 2 and cross out all the multiples of 2. 
Step 3: go to number 3 and encircle it and repeat the method that we did with number 2, i.e. cross out all the multiples of 3. 
Step 4: repeat the steps given in step 2 and step 3 with the remaining numbers 
Result: The encircled numbers are the prime numbers and the crossed out numbers are the composite numbers. 
This method was given by Greek mathematician Eratosthenes in third century B.C. This method is known as the Sieve of Eratosthenes. 


Answer 2

LEt,

2*3+5=6+5

=11

Hence factors of 11=(1,11)

So, 11 has 1 and itself as factor

Hence it is prime