Is 1243 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, 3 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, 6 is divisible by 1, 2, 3, and 6, 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 1243 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 1243 has more than two factors, it is not a prime number. Several methods are used to distinguish between prime and composite numbers. A few 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 prime and composite numbers. 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 1243 is prime or composite.

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

Step 2: Divide 1243 by 2. It is not divisible by 2.

Step 3: Divide 1243 by 3. The sum of the digits (1+2+4+3) is 10, which is not divisible by 3, so 1243 is not divisible by 3.

Step 4: Continue checking divisibility by subsequent prime numbers (5, 7, 11, ...) up to the square root of 1243.

Step 5: When we divide 1243, we find it is divisible by 7 because 1243 ÷ 7 = 177.

Since 1243 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: 1243 is not divisible by 2 as it is an odd number.

Divisibility by 3: The sum of the digits in 1243 is 10, which is not divisible by 3.

Divisibility by 5: The unit’s place digit is not 0 or 5, so it is not divisible by 5.

Divisibility by 7: Using a divisibility rule for 7, we find that 1243 is divisible by 7, as 1243 ÷ 7 = 177.

Since 1243 is divisible by 7, 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 numbers in a grid.

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 desired range. Through this process, we will have a list of prime numbers.

As 1243 is not on the list of prime numbers, it is a composite number.

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

Step 1: We can write 1243 as 7 × 177.

Step 2: In 7 × 177, 177 is a composite number. Further, break down 177 into prime factors.

Step 3: The factorization becomes 7 × 3 × 59. Now we get the product consisting of only prime numbers.

Hence, the prime factorization of 1243 is 7 × 3 × 59.

• 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, 11 is a prime number.
  
   
• Factors: The numbers that divide the number exactly without leaving a remainder are called factors. For example, the factors of 8 are 1, 2, 4, and 8 because they divide 8 completely.
  
   
• Prime factorization: The process of expressing a number as a product of its prime factors. For example, the prime factorization of 18 is 2 × 3 × 3.
  
   
• Divisibility rules: Rules that help determine whether one number is divisible by another without performing division. For example, a number is divisible by 3 if the sum of its digits is divisible by 3.