Is 1302 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 1302 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 1302 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 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 1302 is prime or composite.

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

Step 2: Divide 1302 by 2. It is divisible by 2, so 2 is a factor of 1302.

Step 3: Divide 1302 by 3. The sum of the digits (1+3+0+2=6) is divisible by 3, so 3 is a factor of 1302.

Step 4: You can simplify checking divisors up to 1302 by finding the root value. We then need to only check divisors up to the root value.

Step 5: When we divide 1302 by 2 and 3, it is divisible by both.

Since 1302 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 in the ones' place value is 2, which is even, meaning that 1302 is divisible by 2.

Divisibility by 3: The sum of the digits in the number 1302 is 6. Since 6 is divisible by 3, 1302 is also divisible by 3.

Divisibility by 5: The unit’s place digit is 2. Therefore, 1302 is not divisible by 5.

Divisibility by 7, 11, and others can be checked similarly if necessary. Since 1302 is divisible by 2 and 3, 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 systematic range.

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.

Since 1302 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 1302 as 2 × 651.

Step 2: In 2 × 651, 651 is a composite number. Further, break the 651 into 3 × 217.

Step 3: Now we get the product consisting of 2 × 3 × 217.

The prime factorization of 1302 is 2 × 3 × 217.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers. For example, 1302 is a composite number because it is divisible by 1, 2, 3, 6, 217, 434, 651, and 1302.

• Prime numbers: Natural numbers greater than 1 that have no divisors other than 1 and itself. For example, 13 is a prime number. 

• Divisibility rules: A set of shortcuts to help determine if a number is divisible by another number without performing extensive division.

• Prime factorization: The process of expressing a number as the product of its prime factors.

• Co-prime numbers: Two numbers are co-prime if their greatest common divisor (GCD) is 1. For example, 8 and 9 are co-prime numbers.