Is 877 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 877 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 877 has only two factors, it is a prime number. 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 877 is prime or composite.

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

Step 2: Divide 877 by 2. It is not divisible by 2, so 2 is not a factor of 877.

Step 3: Divide 877 by 3. It is not divisible by 3, so 3 is not a factor of 877.

Step 4: You can simplify checking divisors up to 877 by finding the root value. We then need to only check divisors up to the root value.

Step 5: Continue checking divisibility with prime numbers up to approximately 29 (since 29² is 841, which is less than 877).

Since 877 is not divisible by any of these prime numbers, it has only two divisors: 1 and 877. Hence, 877 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 877 is odd, so it is not divisible by 2.

Divisibility by 3: The sum of the digits in the number 877 is 22. Since 22 is not divisible by 3, 877 is also not divisible by 3.

Divisibility by 5: The unit’s place digit is 7. Therefore, 877 is not divisible by 5.

Divisibility by 7: The last digit in 877 is 7. To check divisibility by 7, double the last digit (7 × 2 = 14). Then, subtract it from the rest of the number (87 - 14 = 73). Since 73 is not divisible by 7, 877 is also not divisible by 7.

Divisibility by 11: In 877, the sum of the digits in odd positions is 14, and the sum of the digits in even positions is 7. The difference is 7, which is not divisible by 11.

Since 877 is not divisible by any of these numbers, 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 1 to 1000 in rows and 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. 877 is present in the list of prime numbers, 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.

Step 1: Start dividing 877 by the smallest prime number.

Step 2: Since 877 is not divisible by any prime number up to the square root of 877, it cannot be factored further.

Step 3: Therefore, 877 is a prime number.

• 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 number: A natural number greater than 1 that has no positive divisors other than 1 and itself.

• Divisibility rules: Rules that help determine if a number is divisible by another number without performing the division.

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

• Co-prime numbers: Two numbers are co-prime if their greatest common divisor (GCD) is 1. ```