Is 1481 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 1481 has only two factors, it is a prime number.

The characteristic of a prime number is that it has only two divisors: 1 and itself. Since 1481 is divisible only by 1 and 1481, it is a prime number. A few methods are used to distinguish between prime and composite numbers. Some 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 prime and composite numbers. -

• 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 1481 is prime or composite.

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

Step 2: Check divisibility by numbers up to the square root of 1481 (approximately 38.5).

Step 3: 1481 is not divisible by any number other than 1 and itself.

Since 1481 has only 2 divisors, it is a prime 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: 1481 is odd, so it is not divisible by 2. 

Divisibility by 3: The sum of the digits in 1481 is 14. Since 14 is not divisible by 3, 1481 is not divisible by 3. 

Divisibility by 5: The unit’s place digit is 1, so 1481 is not divisible by 5. 

Divisibility by 7, 11, 13, etc.: Similar checks can be made for divisibility by other primes up to the square root of 1481.

Since 1481 is not divisible by any number other than 1 and itself, it is a prime 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 in a systematic range.

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 end of the range. Through this process, we will have a list of prime numbers.

Since 1481 is not divisible by any smaller prime numbers up to its square root, it is a prime 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: Check divisibility of 1481 by smaller prime numbers such as 2, 3, 5, 7, etc.

Step 2: Since 1481 is not divisible by any prime numbers other than 1 and itself, 1481 is a prime number.

• Prime numbers: Natural numbers greater than 1 that have no divisors other than 1 and themselves. 

• Composite numbers: Natural numbers greater than 1 that are divisible by more than two numbers. 

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

• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer. 

• Factors: Numbers that divide another number exactly without leaving a remainder.