Is 1482 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 1482 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 1482 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 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 1482 is prime or composite.

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

Step 2: Divide 1482 by 2. It is divisible by 2, so 2 is a factor of 1482.

Step 3: Divide 1482 by 3. The sum of its digits (1 + 4 + 8 + 2 = 15) is divisible by 3, so 3 is a factor of 1482.

Step 4: You can simplify checking divisors up to 1482 by finding the square root value. We then need to only check divisors up to the square root value.

Since 1482 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 2, which is even, meaning that 1482 is divisible by 2. 

Divisibility by 3: The sum of the digits in the number 1482 is 15. Since 15 is divisible by 3, 1482 is divisible by 3. 

Divisibility by 5: The unit’s place digit is not 0 or 5, so 1482 is not divisible by 5. Since 1482 is divisible by 2 and 3, 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 up to an approximate limit that includes 1482.

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

Step 3: Mark small prime numbers (like 2, 3, 5) and cross out their multiples.

Step 4: Continue marking primes and crossing out multiples until the list is complete. Through this process, we will have a list of prime numbers.

1482 is not present in the list of prime numbers, 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 1482 as 2 × 741.

Step 2: In 2 × 741, 741 is a composite number. Further, break 741 into 3 × 247.

Step 3: Now, further break down 247 into 13 × 19.

Hence, the prime factorization of 1482 is 2 × 3 × 13 × 19.

• 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 factorization: Breaking down a number into its basic prime number components, such as 1482 = 2 × 3 × 13 × 19.

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

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

• Co-prime numbers: Two numbers with no common factors other than 1.