Is 1495 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.
   
• As 1495 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 1495 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers. 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 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 1495 is prime or composite.

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

Step 2: Divide 1495 by 5. It is divisible by 5, so 5 is a factor of 1495.

Step 3: Divide 1495 by 3. It is not divisible by 3, so 3 is not a factor of 1495.

Step 4: You can simplify checking divisors up to the root value of 1495. We then need to only check divisors up to the root value.

Step 5: When we divide 1495 by 5 and 299 (1495 divided by 5), it is divisible by 5 and 299.

Since 1495 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 is 5, which is odd. Thus, 1495 is not divisible by 2.

Divisibility by 3: The sum of the digits in the number 1495 is 19. Since 19 is not divisible by 3, 1495 is also not divisible by 3.

Divisibility by 5: The unit’s place digit is 5. Therefore, 1495 is divisible by 5.

Divisibility by 7: To check divisibility by 7, multiply the last digit by 2 (5 × 2 = 10) and subtract it from the rest of the number (149 - 10 = 139). Since 139 is not divisible by 7, 1495 is also not divisible by 7.

Since 1495 is divisible by 5, 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 a suitable range in 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 complete the list. Through this process, the list of prime numbers is generated.

1495 is not present in such a list, so 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 1495 as 5 × 299.

Step 2: In 5 × 299, 299 is a composite number. Further breaking down 299 results in 13 × 23.

Step 3: Now we have the product consisting of only prime numbers.

Hence, the prime factorization of 1495 is 5 × 13 × 23.

• 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 12 is divisible by 1, 2, 3, 4, 6, and 12.
   
• Prime numbers: Natural numbers greater than 1 with no divisors other than 1 and itself are prime numbers. For example, 7 is a prime number.
   
• Divisibility: A number is divisible by another if dividing them results in an integer without a remainder. For example, 10 is divisible by 5.
   
• Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 30 is 2 × 3 × 5.
   
• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer.