Is 1262 a Prime Number?

There are two primary types of numbers — Prime numbers and composite numbers — depending on the number of factors they have.

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 only by 1 and itself.

A composite number is a positive number that is divisible by more than two numbers. For instance, 6 is divisible by 1, 2, 3, and 6, making it a composite number.

Some properties of prime numbers include:

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 1262 has more than two factors, it is not a prime number.

The defining characteristic of a prime number is that it has only two divisors: 1 and itself. Since 1262 has more than two factors, it is not a prime number. Several methods can be used to differentiate between prime and composite numbers. These methods include:

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

This method involves counting the number of divisors to categorize numbers as prime or composite. Based on the count of the divisors, we can categorize numbers as follows:

If there are only 2 divisors, the number is prime.

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

Let’s check whether 1262 is prime or composite.

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

Step 2: Divide 1262 by 2. It is divisible by 2, so 2 is a factor of 1262.

Step 3: Divide 1262 by 3. It is not divisible by 3, so 3 is not a factor of 1262.

Step 4: You can simplify checking divisors up to 1262 by finding the square root value. We then need to only check divisors up to this value.

Step 5: When we divide 1262 by 2 and other numbers up to its square root, it is divisible by 2 and other numbers.

Since 1262 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. This is called the Divisibility Test Method.

Divisibility by 2: The number in the one's place is 2, an even number, meaning 1262 is divisible by 2.

Divisibility by 3: The sum of the digits in 1262 is 11. Since 11 is not divisible by 3, 1262 is also not divisible by 3.

Divisibility by 5: The unit’s place digit is 2. Therefore, 1262 is not divisible by 5.

Divisibility by 7: To check divisibility by 7, use the rule: double the last digit (2 × 2 = 4), and subtract it from the rest of the number (126 - 4 = 122). Since 122 is not divisible by 7, 1262 is also not divisible by 7.

Divisibility by 11: In 1262, the alternating sum of the digits (1 - 2 + 6 - 2) equals 3, which is not divisible by 11. Since 1262 is divisible by 2 and other factors, 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 these steps:

Step 1: Write numbers from 1 to 100 in 10 rows and 10 columns.

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

Step 3: Mark 2 as a prime number and cross out all its multiples.

Step 4: Mark 3 as a prime number and cross out all its multiples.

Step 5: Repeat this process until you reach the table consisting of marked and crossed boxes, except for 1. Through this process, we will have a list of prime numbers from 1 to 100.

Since 1262 is not on this list, it is not a prime number, and it is not needed in this range, confirming it's composite.

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

Step 1: We can write 1262 as 2 × 631.

Step 2: In 2 × 631, check if 631 is a composite number. Further, check divisibility for smaller prime numbers.

Step 3: If 631 is not divisible by any smaller prime numbers (it's a prime itself), then the prime factorization of 1262 is 2 × 631.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers. For example, 12 is a composite number because it is divisible by 1, 2, 3, 4, 6, and 12.
  
   
• Prime numbers: Natural numbers greater than 1 that are divisible only by 1 and themselves. For example, 7 is a prime number because it has only two factors: 1 and 7.
  
   
• Factors: Numbers that divide another number exactly without leaving a remainder. For example, the factors of 4 are 1, 2, and 4.
  
   
• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specific integer.
  
   
• Prime factorization: The expression of a number as the product of its prime factors. For example, 18 can be expressed as 2 × 3 × 3.