Is 292 a Prime Number?

There are two main types of numbers —

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 such as: 

• 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.
   
• Since 292 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 292 has more than two factors, it is not a prime number. Several methods can be used to distinguish between prime and composite numbers. Some of these methods include:

• 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 either prime or composite.

• If there is a total count of only 2 divisors, then the number is prime. 
   
• If the count is more than 2, then the number is composite.

Let’s check whether 292 is prime or composite.

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

Step 2: Divide 292 by 2. It is divisible by 2, so 2 is a factor of 292.

Step 3: Divide 292 by 3. It is not divisible by 3, so 3 is not a factor of 292.

Step 4: You can simplify checking divisors up to 292 by finding the square root. We then need to only check divisors up to this root value.

Since 292 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. This is called the Divisibility Test Method.

Divisibility by 2: The number in the ones place value is 2, which is an even number, meaning 292 is divisible by 2.

Divisibility by 3: The sum of the digits in 292 is 13. Since 13 is not divisible by 3, 292 is not divisible by 3.

Divisibility by 5: The unit’s place digit is not 0 or 5, so 292 is not divisible by 5.

Divisibility by 7: For 292, doubling the last digit (2×2=4) and subtracting from the rest of the number (29-4=25) shows that 25 is not divisible by 7, so 292 is not divisible by 7.

Divisibility by 11: The alternating sum of the digits (2 - 9 + 2 = -5) is not divisible by 11, so 292 is not divisible by 11.

Since 292 is divisible by 2, it has more than two factors, and 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 these steps:

Step 1: Write numbers from 1 to 100 in 10 rows and 10 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 multiples of 2.

Step 4: Mark 3 because it is a prime number and cross out all multiples of 3.

Step 5: Repeat this process until the table consists of marked and crossed boxes, except for 1. Through this process, we will have a list of prime numbers from 1 to 100.

Since 292 is not in the list of prime numbers, it is a composite number.

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

Step 1: We can write 292 as 2 × 146.

Step 2: In 2 × 146, 146 is a composite number. Further, break 146 into 2 × 73.

Step 3: Now we get the product consisting entirely of prime numbers.

Hence, the prime factorization of 292 is 2 × 2 × 73.

• 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 it is divisible by 1, 2, 3, 4, 6, and 12.
   
• Prime numbers: Natural numbers greater than 1 that have exactly two distinct positive divisors, 1 and the number itself.
   
• Divisibility Test: A set of rules to determine if a number is divisible by another number without performing division.
   
• Prime Factorization: The process of expressing a number as the product of its prime factors.
   
• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer.