Is 291 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 have 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 291 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 291 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers. Some 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 numbers as prime or composite.

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 291 is prime or composite.

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

Step 2: Divide 291 by 2. It is not divisible by 2, so 2 is not a factor of 291.

Step 3: Divide 291 by 3. It is divisible by 3, so 3 is a factor of 291.

Step 4: You can simplify checking divisors up to 291 by finding the square root value. We then need to only check divisors up to that value.

Step 5: When we divide 291 by 3 and other numbers, it is divisible by 3.

Since 291 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 1. Since it is odd, 291 is not divisible by 2.

Divisibility by 3: The sum of the digits in the number 291 is 12. Since 12 is divisible by 3, 291 is also divisible by 3.

Divisibility by 5: The unit’s place digit is 1. Therefore, 291 is not divisible by 5.

Divisibility by 7: To check divisibility by 7, double the last digit (1 × 2 = 2). Then, subtract it from the rest of the number (29 - 2 = 27). Since 27 is divisible by 7, 291 is also divisible by 7.

Divisibility by 11: In 291, the sum of the digits in odd positions is 3, and the sum of the digits in even positions is 9. Since the difference (6) is not divisible by 11, 291 is not divisible by 11.

Since 291 is divisible by 3 and 7, 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 from 1 to 300 in rows and 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 300. 291 is not present in the list of prime numbers, so 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 291 as 3 × 97.

Step 2: 3 and 97 are both prime numbers.

Step 3: Hence, the prime factorization of 291 is 3 × 97.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 12 is a composite number because 12 is divisible by 1, 2, 3, 4, 6, and 12.
   
• Divisibility rules: Guidelines to determine if one number is divisible by another without performing division.
   
• Prime factorization: The process of expressing a number as a product of its prime factors.
   
• Sieve of Eratosthenes: A simple algorithm to find all prime numbers up to a specified integer.
   
• Co-prime numbers: Two numbers are co-prime if their greatest common divisor is 1, meaning they have no common factors other than 1.