Is 943 a Prime Number?

There are two types of numbers, mostly —

Prime numbers and composite numbers, depending on the number of factors.

A prime number is a natural number that is divisible only by 1 and itself.

For example, 5 is a prime number because it is divisible by 1 and itself.

A composite number is a positive number that is divisible by more than two numbers.

For example, 8 is divisible by 1, 2, 4, and 8, making it a composite number.

Prime numbers follow a few properties like:

• Prime numbers are positive numbers always greater than 1.
   
• 2 is the only even prime number. 
   
• They have only two factors: 1 and the number itself.
   
• Any two distinct prime numbers are co-prime numbers because they have only one common factor, which is 1.
   
• As 943 has more than two factors, it is not a prime number.
  

The characteristic of a prime number is that it has only two divisors: 1 and itself. Since 943 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers. Some methods are:

• Counting Divisors Method
   
• Divisibility Test
   
• Prime Number Chart 
   
• Prime Factorization

The method in which we count the number of divisors to categorize the numbers as prime or composite is called the counting divisors method. Based on the count of the divisors, we categorize numbers as prime or composite.

• If there is a total count of only 2 divisors, then the number would be prime.
   
• If the count is more than 2, then the number is composite.

Let’s check whether 943 is prime or composite.

Step 1: All numbers are divisible by 1 and itself.

Step 2: Divide 943 by 2. It is not divisible by 2, so 2 is not a factor of 943.

Step 3: Divide 943 by 3. The sum of the digits (9 + 4 + 3 = 16) is not divisible by 3, so 3 is not a factor of 943.

Step 4: Continue testing divisibility by prime numbers up to the approximate square root of 943, which is around 30.7.

Step 5: 943 is divisible by 23 (943 ÷ 23 = 41).

Since 943 has more than 2 divisors, it is a composite number.

We use a set of rules to check whether a number is divisible by another number completely or not. It is called the Divisibility Test Method.

Divisibility by 2: The number in the ones place is 3. Since it is not even, 943 is not divisible by 2.

Divisibility by 3: The sum of the digits in 943 is 16. Since 16 is not divisible by 3, 943 is also not divisible by 3.

Divisibility by 5: The unit’s place digit is 3. Therefore, 943 is not divisible by 5.

Divisibility by 7: Doubling the last digit (3 × 2 = 6) and subtracting from the rest (94 - 6 = 88) shows that 88 is divisible by 8, not by 7, so 943 is not divisible by 7.

Divisibility by 11: The difference between the sum of the digits in odd positions and even positions is 0 (9 + 3 - 4 = 8), which is not divisible by 11.

Divisibility by 23: 943 is divisible by 23 (943 ÷ 23 = 41).

Since 943 is divisible by 23 and 41, it has more than two factors. Therefore, it is a composite number.

The prime number chart is a tool created by using a method called “The Sieve of Eratosthenes.” In this method, we follow the following steps.

Step 1: Write 1 to 1000 in rows and columns.

Step 2: Leave 1 without coloring or crossing, as it is neither prime nor composite.

Step 3: Mark 2 because it is a prime number and cross out all the multiples of 2.

Step 4: Mark 3 because it is a prime number and cross out all the multiples of 3.

Step 5: Repeat this process until you reach the table consisting of marked and crossed boxes, except 1.

Through this process, we will have a list of prime numbers from 1 to 1000. 943 is not present in the list of prime numbers, so it is a composite number.

Prime factorization is a process of breaking down a number into prime factors and then multiplying those factors to obtain the original number.

Step 1: We can write 943 as 23 × 41.

Step 2: Both 23 and 41 are prime numbers.

Therefore, the prime factorization of 943 is 23 × 41.

• Composite Numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 12 is a composite number because 12 is divisible by 1, 2, 3, 4, 6, and 12.
   
• Prime Numbers: Numbers greater than 1 that have no divisors other than 1 and themselves. For example, 7 is a prime number.
   
• Divisibility Rules: Guidelines to determine if one number is divisible by another without performing division.
   
• Sieve of Eratosthenes: An ancient algorithm to find all prime numbers up to any given limit.
   
• Prime Factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 18 is 2 × 3 × 3.