Is 1265 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 1265 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 1265 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers:

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

In the counting divisors method, we count the number of divisors to categorize the numbers as prime or composite. 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 1265 is prime or composite.

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

Step 2: Divide 1265 by 5. It is divisible by 5, so 5 is a factor of 1265.

Step 3: Divide 1265 by 11. It is divisible by 11, so 11 is a factor of 1265.

Step 4: You can simplify checking divisors up to 1265 by finding the root value. We then need to only check divisors up to the root value.

Since 1265 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: 1265 is not divisible by 2, as it is not even.

- Divisibility by 3: The sum of the digits in the number 1265 is 14. Since 14 is not divisible by 3, 1265 is not divisible by 3.

- Divisibility by 5: The unit’s place digit is 5. Therefore, 1265 is divisible by 5.

- Divisibility by 11: The alternating sum of the digits (1 - 2 + 6 - 5 = 0) is divisible by 11, hence 1265 is divisible by 11. Since 1265 is divisible by 5 and 11, it has more than two factors.

Therefore, it is a composite number.

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

Step 1: Write 1 to 100 in 10 rows and 10 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 100.

However, since 1265 is not present in the list of prime numbers, 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 write 1265 as 5 × 253.

Step 2: In 5 × 253, 253 is a composite number. Further, break 253 into 11 × 23.

Step 3: Now we get the product consisting of only prime numbers.

Hence, the prime factorization of 1265 is 5 × 11 × 23.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 1265 is a composite number because it is divisible by 1, 5, 11, 23, and 1265.
  
   
• Divisibility: The ability for one number to be divided by another without a remainder. For example, 1265 is divisible by 5.
  
   
• Prime factorization: Breaking down a number into its prime number multipliers. For example, 1265 can be factorized into 5 × 11 × 23.
  
   
• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer.
  
   
• Co-prime numbers: Two numbers that have only 1 as their greatest common divisor. For example, 9 and 28 are co-prime.