Is 1487 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.
• Since 1487 has exactly two factors, it is a prime number.

The characteristic of a prime number is that it has only two divisors: 1 and itself. Since 1487 has exactly two factors, it is a prime number. A few 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 1487 is prime or composite.

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

Step 2: Divide 1487 by 2. It is not divisible by 2, so 2 is not a factor of 1487.

Step 3: Check divisibility by other numbers such as 3, 5, 7, etc., up to the square root of 1487.

Since 1487 is not divisible by any number other than 1 and itself, 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: The number in the ones' place value is 7, which is odd, so 1487 is not divisible by 2.

Divisibility by 3: The sum of the digits in the number 1487 is 20. Since 20 is not divisible by 3, 1487 is also not divisible by 3.

Divisibility by 5: The unit’s place digit is 7. Therefore, 1487 is not divisible by 5.

Divisibility by 7: Performing the divisibility test for 7 reveals that 1487 is not divisible by 7.

Since 1487 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 range, for example, 1 to 2000.

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 for all prime numbers up to the square root of the maximum number in your range.

Through this process, 1487 remains unmarked, indicating that 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 1487 by prime numbers like 2, 3, 5, and so on.

Step 2: Since 1487 is not divisible by any other number than 1 and itself, it remains as 1487 × 1.

Hence, 1487 is a prime number as it cannot be broken down into other prime numbers.

• Prime Numbers: Natural numbers greater than 1 that are divisible only by 1 and themselves. For example, 1487 is a prime number.

• Composite Numbers: Natural numbers greater than 1 that are divisible by more than two numbers. For example, 12 is a composite number.

• Divisibility: A concept in mathematics used to determine if one integer is divisible by another.

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

• Prime Factorization: The process of expressing a number as a product of its prime factors.