Is 295 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 follow 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.
   
• As 295 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 295 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 295 is prime or composite.

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

Step 2: Divide 295 by 2. It is not divisible by 2, so 2 is not a factor of 295.

Step 3: Divide 295 by 3. It is not divisible by 3, so 3 is not a factor of 295.

Step 4: Divide 295 by 5. It is divisible by 5, so 5 is a factor of 295.

Step 5: When we check further, 295 is divisible by 59 as well, confirming it has more than 2 divisors.

Since 295 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 5. Since 5 is not even, 295 is not divisible by 2.

Divisibility by 3: The sum of the digits in the number 295 is 16. Since 16 is not divisible by 3, 295 is also not divisible by 3.

Divisibility by 5: The unit’s place digit is 5. Therefore, 295 is divisible by 5.

Divisibility by 7, 11, and other numbers can be checked similarly, but we find that 59 is a divisor of 295.

Since 295 is divisible by 5 and 59, 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 these steps:

Step 1: Write 1 to 100 in 10 rows and 10 columns (for smaller numbers). For 295, we only consider prime numbers up to its square root.

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: Continue this process for other numbers like 5, 7, etc. Through this process, we list the prime numbers.

295 is not on this list, confirming 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 295 as 5 × 59.

Step 2: Both 5 and 59 are prime numbers.

Step 3: Hence, the prime factorization of 295 is 5 × 59.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than two numbers are called composite numbers. For example, 12 is a composite number because 12 is divisible by 1, 2, 3, 4, 6, and 12.
   
• Prime number: A natural number greater than 1 that is not divisible by any other numbers except 1 and itself.
   
• Divisibility rules: A set of rules that help determine whether a number is divisible by another number.
   
• Prime factorization: The process of determining which prime numbers multiply together to create the original number.
   
• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a given limit.