Is 294 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.
   
• Since 294 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 294 has more than two factors, it is not a prime number. Various methods can be used to distinguish between prime and composite numbers. Some 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 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 294 is prime or composite.

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

Step 2: Divide 294 by 2. It is divisible by 2, so 2 is a factor of 294.

Step 3: Divide 294 by 3. It is divisible by 3, so 3 is a factor of 294.

Step 4: You can simplify checking divisors by finding the square root of 294 and checking divisors up to that value.

Step 5: Continue checking divisibility by other numbers such as 5, 7, etc.

Since 294 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 4. Since 4 is even, 294 is divisible by 2.

Divisibility by 3: The sum of the digits in the number 294 is 15. Since 15 is divisible by 3, 294 is also divisible by 3.

Divisibility by 5: The unit’s digit is not 0 or 5, so 294 is not divisible by 5.

Divisibility by 7: For divisibility by 7, double the last digit (4 × 2 = 8) and subtract it from the rest (29 - 8 = 21). Since 21 is divisible by 7, 294 is also divisible by 7.

Divisibility by 11: The alternating sum of the digits is 2 - 9 + 4 = -3, which is not divisible by 11. Since 294 is divisible by several numbers, 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 100 (or more) in several 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 finish marking and crossing the relevant numbers. Through this process, we get a list of prime numbers.

Since 294 is not present in the list of prime numbers, it is a composite number.

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

Step 1: We can write 294 as 2 × 147.

Step 2: In 2 × 147, 147 is a composite number. Further, break 147 into 3 × 49.

Step 3: Break 49 into 7 × 7.

Step 4: Now, we have the product consisting of only prime numbers.

Hence, the prime factorization of 294 is 2 × 3 × 7 × 7.

• Composite Numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 294 is a composite number because it is divisible by 1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, and 294.
   
• Divisibility Rules: A set of guidelines to determine whether one number is divisible by another without performing division.
   
• Prime Factorization: The process of expressing a number as the product of its prime factors.
   
• Even numbers: Numbers divisible by 2 without a remainder. For example, 294 is an even number.
   
• Prime numbers: Natural numbers greater than 1 that have no divisors other than 1 and themselves. For example, 3 and 7 are prime numbers.