Is 1264 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 1264 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 1264 has more than two factors, it is not a prime number. Few 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 1264 is prime or composite.

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

Step 2: Divide 1264 by 2. It is divisible by 2, so 2 is a factor of 1264.

Step 3: Continue with other numbers like 3, 4, 5, and so on, until you find more divisors.

Step 4: You can simplify checking divisors up to 1264 by finding the square root value. We then need to only check divisors up to the square root value.

Since 1264 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 1264 ends in 4, which is an even number, so it is divisible by 2.

- Divisibility by 3: The sum of the digits in the number 1264 is 13. Since 13 is not divisible by 3, 1264 is not divisible by 3.

- Divisibility by 5: The unit’s place digit is not 0 or 5, so 1264 is not divisible by 5.

- Divisibility by 7: You can apply the divisibility rule for 7 to determine if 1264 is divisible by 7.

- Divisibility by 11: You can apply the divisibility rule for 11 to determine if 1264 is divisible by 11. Since 1264 is divisible by more than just 1 and itself, 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 sequence, for example, up to 1300.

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 end of the list. Through this process, we will have a list of prime numbers up to 1300.

Since 1264 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 multiplying those factors to obtain the original number.

Step 1: We can write 1264 as 2 × 632.

Step 2: In 2 × 632, 632 is a composite number. Further, break 632 into 2 × 316.

Step 3: Continue breaking down the numbers until you get the product consisting of only prime numbers.

For 1264, this results in 2 × 2 × 2 × 2 × 79.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 1264 is a composite number because it is divisible by 1, 2, 4, 8, 16, 79, 158, 316, 632, and 1264.
  
   
• Factors: The numbers that divide the number exactly without leaving a remainder are called factors. For example, the factors of 1264 are 1, 2, 4, 8, 16, 79, 158, 316, 632, and 1264 because they divide 1264 completely.
  
   
• Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 1264 is 2 × 2 × 2 × 2 × 79.
  
   
• Divisibility rules: A set of rules that help determine whether a number is divisible by another without performing division.
  
   
• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer.