Is 43 a Prime Number?

You should know that all numbers can be classified into prime or composite numbers.43 is a prime number, since factors of 43 are 1 and 43 only. That means it is a prime number, since prime numbers have only 1 and the number itself as their factors. So, we can say that 43 is a prime number.

We will now check through various methods that 43 is a prime number. Let’s proceed.

• Counting Divisors Method

• Divisibility Test

• Prime Number Chart

• Prime Factorization Method
   

The only condition this method involves is that a particular number is prime if and only if it has two distinct integers as its divisors. In case of 43, the distinct divisors are: 1 and 43. 
 

In the divisibility method, we have to check 43 with different numbers whether 43 is divisible by those numbers or not. The rule is, if 43 is divisible by any number that falls between 2 and the square root of 43 itself, it is composite, or else it is prime. 

Testing the same in case of 43:

Step 1: Checking divisibility by 2

Any even number is divisible by 2. 43 is not an even number, so it is not divisible by 2.

Step 2: Checking divisibility by 3.

Any number is divisible by 3 if the sum of the digits is divisible by 3. 

4+3=7, which is not divisible by 3, so, 43 is also not divisible by 3.

Step 3: Checking divisibility by 4.

Any number is divisible by 4 if its last two digits are divisible by 4. 43’s last two digits are 43 itself, and it is not divisible by 4.

Step 4: Checking divisibility by 5.

Any number is divisible by 5 if its last digit is either 0 or 5. 43’s last digit is 3, hence, 43 is not divisible by 5.

Step 5: Check divisibility by 6.

Any number is divisible by 6, if and only if it is divisible by 2 and 3 both. 
43 is neither divisible by 2 nor by 3, as we checked above.

Also, the square root of 43 is less than 7, so no need to check divisibility greater than 6.

We can conclude that 43 is a prime number and 43 is not divisible by numbers other than 1 and 43.
 

The list of prime numbers up to 50 are → 2,3,5,7,11,13,17,19, 23,29,31,37,41,43,47 
Following the above chart for reference, we can see that 43 is in the list. Hence, 43 is a prime number.
 

Prime factorization of 43

43 = 43×1 

43 is not being easily factored into smaller factors, clearly making it a prime number. 

• Cryptography: This is the branch which deals with cybersecurity, applying encoding-decoding methods.

• Prime Factorization: The process of breaking down a number into its prime factors is called Prime Factorization. 

• Composite numbers: Composite numbers are numbers with multiples that are not just 1 and the number itself.

• Twin prime numbers: Twin primes are those prime number pairs that have a difference of 2. 

• Perfect Divisor: Integers that divide into numbers, leaving no remainders behind.