Is 887 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.
• To determine if 887 is a prime number, we need to confirm it has only two factors.

The characteristic of a prime number is that it has only two divisors: 1 and itself. Since 887 has exactly two factors (1 and 887 itself), 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 would be prime. -
• If the count is more than 2, then the number is composite.

Let’s check whether 887 is prime or composite.

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

Step 2: Check divisibility up to the square root of 887, approximately 29.8 (round down to 29).

Step 3: 887 is not divisible by any prime numbers less than or equal to 29, such as 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29.

Since 887 has only 2 divisors (1 and 887), 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: 887 is odd, so it is not divisible by 2. -

Divisibility by 3: The sum of the digits in 887 is 23, which is not divisible by 3. -

Divisibility by 5: 887 does not end in 0 or 5, so it is not divisible by 5. -

Divisibility by 7, 11, 13, 17, 19, 23, and 29: Through direct division, 887 is not divisible by any of these primes.

Since 887 is not divisible by any prime number up to its approximate square root, 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 up to at least 900.

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

Step 3: Mark all prime numbers and cross out all their multiples up to 900. Through this process, we have a list of prime numbers, and 887 will be found in this list, confirming 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. Since 887 cannot be written as a product of any other numbers besides 1 and 887, it remains prime.

• Prime numbers: Natural numbers greater than 1 that have no divisors other than 1 and themselves. For example, 887 is a prime number. 

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers. For example, 12 is a composite number because it is divisible by 1, 2, 3, 4, 6, and 12. 

• Divisibility rules: Guidelines used to determine whether one number is divisible by another without performing division. For example, a number is divisible by 3 if the sum of its digits is divisible by 3. 

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

• Co-prime numbers: Two numbers with no common factors other than 1. For example, 8 and 15 are co-prime.