Is 1494 a Prime Number?

Numbers can typically be classified as either prime numbers or composite numbers, depending on the number of factors they have.

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.

Some properties of prime numbers include: -

• 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 because they have only one common factor, which is 1.
   
• As 1494 has more than two factors, it is not a prime number.

The defining characteristic of a prime number is that it has only two divisors: 1 and itself. Since 1494 has more than two factors, it is not a prime number. There are various methods to distinguish between prime and composite numbers, such as:

• Counting Divisors Method 
   
• Divisibility Test 
   
• Prime Number Chart 
   
• Prime Factorization

The counting divisors method involves counting the number of divisors a number has to determine if it is prime or composite.

• If there are exactly 2 divisors, the number is prime.
   
• If there are more than 2, the number is composite.
   

Let’s check whether 1494 is prime or composite.

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

Step 2: Divide 1494 by 2. It is divisible by 2, so 2 is a factor of 1494.

Step 3: Divide 1494 by 3. It is divisible by 3, so 3 is a factor of 1494.

Step 4: To simplify, consider checking divisors up to the square root of 1494.

Step 5: When we divide 1494 by 2, 3, and several other numbers, it is fully divisible by several of them.

Since 1494 has more than 2 divisors, it is a composite number.

The Divisibility Test Method involves using rules to check whether a number is divisible by another number without leaving a remainder. 

Divisibility by 2: The number in the ones' place is 4, an even number, so 1494 is divisible by 2. 

Divisibility by 3: The sum of the digits in the number 1494 is 18. Since 18 is divisible by 3, 1494 is also divisible by 3.

Divisibility by 5: The unit’s place digit is 4, so 1494 is not divisible by 5. 

Divisibility by 7: Using the rule, 1494 is not divisible by 7.

Divisibility by 11: Applying the divisibility rule for 11, 1494 is not divisible by 11.

Since 1494 is divisible by multiple numbers, it has more than two factors, confirming 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 rows and columns.

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

Step 3: Mark 2 as a prime number and cross out all multiples of 2.

Step 4: Mark 3 as a prime number and cross out all multiples of 3.

Step 5: Repeat this process for other numbers to identify primes up to 100.

Since 1494 is not included in the list of numbers less than 100, nor is it identified as a prime through other methods, it is confirmed as a composite number.

Prime factorization involves breaking down a number into its prime factors. Then, multiplying those factors gives the original number.

Step 1: We can write 1494 as 2 × 747.

Step 2: In 2 × 747, 747 is a composite number. Further, break 747 into 3 × 249.

Step 3: Continue factorization: 249 can be written as 3 × 83.

Step 4: Now we have the prime factors: 2, 3, 3, and 83.

Therefore, the prime factorization of 1494 is 2 × 3 × 3 × 83.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers. For example, 12 is composite because it is divisible by 1, 2, 3, 4, 6, and 12.
   
• Prime numbers: Numbers greater than 1 with exactly two distinct positive divisors: 1 and itself. For example, 5 is prime because it is only divisible by 1 and 5. 
   
• Divisibility rules: Guidelines that help determine if one number is divisible by another without performing the actual division.
   
• Prime factorization: Breaking down a composite number into a product of its prime factors. For example, the prime factorization of 18 is 2 × 3 × 3.
   
• Co-prime numbers: Two numbers with no common factors other than 1. For example, 15 and 28 are co-prime.