Is 882 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 882 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 882 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers. These methods include:

• Counting Divisors Method
• Divisibility Test
• Prime Number Chart
• Prime Factorization

The method in which we count the number of divisors to categorize numbers as prime or composite is called the counting divisors method. Based on the count of the divisors, we categorize numbers as either prime or composite.

• 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 882 is prime or composite.

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

Step 2: Divide 882 by 2. It is divisible by 2, so 2 is a factor of 882.

Step 3: Divide 882 by 3. It is divisible by 3, so 3 is a factor of 882.

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

Step 5: When we divide 882 by other numbers, it is divisible by several, including 2, 3, 6, and more. Since 882 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 value is 2, an even number, which means that 882 is divisible by 2.

Divisibility by 3: The sum of the digits in the number 882 is 18. Since 18 is divisible by 3, 882 is also divisible by 3.

Divisibility by 5: The unit’s place digit is not 0 or 5. Therefore, 882 is not divisible by 5.

Divisibility by 7: Using the rule to check divisibility by 7, 882 is divisible by 7.

Divisibility by 11: In 882, the alternating sum of the digits (8 - 8 + 2) is 2, which is not divisible by 11. Since 882 is divisible by more than two numbers, 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 from 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. 882 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 882 as 2 × 441.

Step 2: In 2 × 441, 441 is a composite number. Further, break 441 into 3 × 147.

Step 3: Now break 147 into 3 × 49.

Step 4: Break 49 into 7 × 7.

Step 5: Now we get the product consisting of only prime numbers. Hence, the prime factorization of 882 is 2 × 3 × 3 × 7 × 7.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 882 is a composite number because it is divisible by multiple numbers.

• Prime factorization: The process of breaking down a number into its prime factors.

• Divisibility test: A set of rules to quickly determine if one number is divisible by another.

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

• Co-prime numbers: Two numbers that have only 1 as their common factor.