Is 1201 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 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.
• 1201 has only two factors, 1 and 1201 itself, so it is a prime number.

The characteristic of a prime number is that it has only two divisors: 1 and itself. Since 1201 has exactly two factors, it is a prime number. Few methods are used to distinguish between prime and composite numbers. A few methods are: -

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 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 1201 is prime or composite. -

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

Step 2: Check divisibility by numbers up to the square root of 1201, which is approximately 34.64. -

Step 3: 1201 is not divisible by any number other than 1 and itself.

Since 1201 has only 2 divisors, it is a prime 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: 1201 is not even. - Divisibility by 3: The sum of the digits (1+2+0+1=4) is not divisible by 3. 

Divisibility by 5: The last digit is not 0 or 5. 

Divisibility by 7: No whole number results from dividing 1201 by 7. 

Divisibility by 11: The alternating sum of digits (1-2+0-1=-2) is not divisible by 11. 

Divisibility by smaller primes: Continue checking with other prime numbers up to 34. Since 1201 is not divisible by any number other than 1 and itself, it is a prime number.

The prime number chart is a tool created by using a method called “The Sieve of Eratosthenes.” This method helps identify prime numbers up to a certain limit. -

Step 1: Write numbers in a grid format. 

Step 2: Leave 1 without coloring or crossing, as it is neither prime nor composite. 

Step 3: Mark 2 and cross out all multiples of 2. 

Step 4: Repeat the process with the next uncrossed number, 3. 

Step 5: Continue until all numbers up to the desired limit have been marked or crossed.

1201 does not appear in any lists of composite numbers generated by this process, confirming it as prime.

Prime factorization is a process of breaking down a number into prime factors. If the number can only be broken down into 1 and itself, it is prime. -

Step 1: Attempt to divide 1201 by prime numbers starting from 2 up to the square root of 1201. -

Step 2: None of these divisions result in a whole number except when divided by 1 or 1201 itself.

Thus, the prime factorization confirms that 1201 is a prime number.

• Prime numbers: Natural numbers greater than 1 that have no divisors other than 1 and themselves.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers.

• Divisibility rules: Guidelines for determining whether one number is divisible by another without performing full 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.