Is 1498 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 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 because they have only one common factor, which is 1. 
   
• Since 1498 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 1498 has more than two factors, it is not a prime number. There are several methods to distinguish between prime and composite numbers, such as:

• 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 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 1498 is prime or composite.

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

Step 2: Divide 1498 by 2. It is divisible by 2, so 2 is a factor of 1498.

Step 3: Divide 1498 by 3. It is not divisible by 3, so 3 is not a factor of 1498.

Step 4: Simplify checking divisors up to the square root of 1498.

Step 5: When dividing 1498 by 2 and other numbers up to its square root, it is divisible by 2, 11, and 136.

Since 1498 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 8, which is even. Therefore, 1498 is divisible by 2.

Divisibility by 3: The sum of the digits in the number 1498 is 22. Since 22 is not divisible by 3, 1498 is also not divisible by 3. 

Divisibility by 5: The unit’s place digit is 8. Therefore, 1498 is not divisible by 5.

Divisibility by 7: To check divisibility by 7, perform further calculations, and find that 1498 is not divisible by 7.

Divisibility by 11: Checking the alternating sum of digits, 1498 is found to be divisible by 11.

Since 1498 has more than two factors, 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 a certain range 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 its multiples.

Step 4: Mark the next unmarked number (3) as prime and cross out all its multiples.

Step 5: Repeat this process until you finish the range. Through this process, we will have a list of prime numbers.

Since 1498 is not on 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 1498 as 2 × 749.

Step 2: In 2 × 749, 749 is a composite number. Further, break down 749 into 11 × 68.

Step 3: Continue factoring 68 into 2 × 34.

Step 4: Further break 34 into 2 × 17. Now we have the product consisting of only prime numbers.

Hence, the prime factorization of 1498 is 2 × 2 × 11 × 17.

• 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 it is divisible by 1, 2, 3, 4, 6, and 12.
   
• Prime Factorization: The process of decomposing a number into a product of prime numbers. For example, the prime factorization of 20 is 2 × 2 × 5.
   
• Divisibility Rules: A set of guidelines used to determine whether a number is divisible by another without performing division. For example, a number is divisible by 3 if the sum of its digits is divisible by 3.
   
• Prime Numbers: Numbers greater than 1 with no divisors other than 1 and themselves. For example, 5 is a prime number.
   
• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer.