Is 1455 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 instance, 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 1455 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 1455 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: 

1. Counting Divisors Method 
2. Divisibility Test 
3. Prime Number Chart 
4. 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 is prime. -
• If the count is more than 2, then the number is composite.

Let’s check whether 1455 is prime or composite. -

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

Step 2: Divide 1455 by 3. The sum of the digits (1 + 4 + 5 + 5 = 15) is divisible by 3, so 3 is a factor of 1455. -

Step 3: Divide 1455 by 5. The last digit is not 0 or 5, so it is not divisible by 5. -

Step 4: You can simplify checking divisors up to 1455 by finding the root value. We then need to only check divisors up to the root value.

Since 1455 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. This is called the Divisibility Test Method. 

Divisibility by 2: 1455 is not even, so it is not divisible by 2. 

Divisibility by 3: The sum of the digits in 1455 is 15, which is divisible by 3. Therefore, 1455 is divisible by 3. 

Divisibility by 5: The unit’s place digit is not 0 or 5, so 1455 is not divisible by 5. 

Divisibility by 11: The alternating sum of the digits (1 - 4 + 5 - 5 = -3) is not divisible by 11, so 1455 is not divisible by 11.

Since 1455 is divisible by numbers other than 1 and itself, it is a composite number.

The prime number chart is a tool created using a method called “The Sieve of Eratosthenes.” In this method, we follow the following steps: -

Step 1: Write 1 to 100 in 10 rows and 10 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 reach the table consisting of marked and crossed boxes, except 1. Through this process, we will have a list of prime numbers from 1 to 100.

Since 1455 is greater than 100, it is not in this list. However, by checking divisibility, we find it is not prime.

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 1455 as 3 × 485. 

Step 2: In 3 × 485, 485 is composite. Further, break 485 into 5 × 97. 

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

Hence, the prime factorization of 1455 is 3 × 5 × 97.

• 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: Numbers greater than 1 that have no other divisors except 1 and themselves.

•  Factors: The numbers that divide another number exactly without leaving a remainder are called factors. For example, the factors of 4 are 1, 2, and 4 because they divide 4 completely. 

• Divisibility rules: Guidelines to determine if one number is divisible by another without performing division. 

• Prime factorization: Breaking down a number into a product of its prime factors.