Is 1202 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 1202 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 1202 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: -

1. Counting Divisors Method 
2. Divisibility Test 
3. Prime Number Chart 
4. 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 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 1202 is prime or composite.

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

Step 2: Divide 1202 by 2. It is divisible by 2, so 2 is a factor of 1202.

Step 3: Divide 1202 by 3. It is not divisible by 3, so 3 is not a factor of 1202.

Step 4: You can simplify checking divisors up to the square root of 1202. Step 5: When we divide 1202 by 2, 601, and other numbers,

since 1202 is divisible by 2 and 601, it has more than 2 divisors, making it a composite number.

We use a set of rules to check whether a number is divisible by another number completely or not. This is called the Divisibility Test Method. -

Divisibility by 2: The number in the ones' place value is 2, which is even, meaning that 1202 is divisible by 2. 

Divisibility by 3: The sum of the digits in the number 1202 is 5. Since 5 is not divisible by 3, 1202 is not divisible by 3. 

Divisibility by 5: The unit’s place digit is 2. Therefore, 1202 is not divisible by 5. -

Divisibility by 7: By applying the divisibility rule for 7, 1202 is not divisible by 7. -

Divisibility by 11: The alternating sum of the digits in 1202 is -1, which is not divisible by 11, so 1202 is not divisible by 11.

Since 1202 is divisible by 2 and 601, 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 from 1 to a certain limit in rows and columns.

Step 2: Leave 1 without marking, 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 up to your desired range. Through this process, we will have a list of prime numbers. 1202 is not present in the list of prime numbers, confirming it is a composite number.

Prime factorization is the process of breaking down a number into its prime factors, then multiplying those factors to obtain the original number.

Step 1: We can write 1202 as 2 × 601.

Step 2: 601 is a prime number and cannot be further broken down into smaller factors.

Step 3: The prime factorization of 1202 is 2 × 601.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 1202 is a composite number because it is divisible by 1, 2, 601, and 1202.

• Prime numbers: Numbers greater than 1 that are only divisible by 1 and themselves.

• Divisibility rule: A shortcut method to determine if one 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.

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