Is 1247 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 1247 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 1247 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers. These methods include:

• 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 is prime.

- If the count is more than 2, then the number is composite.

Let’s check whether 1247 is prime or composite.

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

Step 2: Divide 1247 by 2. It is not divisible by 2, so 2 is not a factor.

Step 3: Divide 1247 by 3. It is not divisible by 3, so 3 is not a factor.

Step 4: You can simplify checking divisors up to the square root of 1247.

Step 5: When we divide 1247 by other numbers up to its square root, we find that it is divisible by 29.

Since 1247 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 1247 is odd, so it is not divisible by 2.

- Divisibility by 3: The sum of the digits in 1247 is 1 + 2 + 4 + 7 = 14. Since 14 is not divisible by 3, 1247 is also not divisible by 3.

- Divisibility by 5: The unit's place digit is 7. Therefore, 1247 is not divisible by 5.

- Divisibility by 7: Doubling the last digit and subtracting it from the rest of the number does not result in a number divisible by 7.

- Divisibility by 11: Alternating sum of digits (1 - 2 + 4 - 7 = -4) is not divisible by 11.

Since 1247 is divisible by 29, it has more than two factors, making it 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 these steps:

Step 1: Write numbers in rows and columns up to a limit.

Step 2: Leave 1 unmarked, as it is neither prime nor composite.

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

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

Step 5: Repeat this process for other prime numbers. Through this process, we will generate a list of prime numbers.

Since 1247 is not in this list, it is a composite number.

Prime factorization is a process of breaking down a number into prime factors. Then multiply those factors to obtain the original number.

Step 1: We can start by dividing 1247 by 29, which is a prime number.

Step 2: Dividing 1247 by 29 gives 43, which is also a prime number.

Step 3: Therefore, the prime factorization of 1247 is 29 × 43.

• 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: Natural numbers greater than 1 with no divisors other than 1 and itself. For example, 5 is a prime number.
  
   
• Divisibility test: A set of rules to determine if one number is divisible by another without performing division.
  
   
• Prime factorization: The expression of a composite number as a product of its prime factors.
  
   
• Sieve of Eratosthenes: An ancient algorithm to find all prime numbers up to a specified integer.