Is 899 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 that is 1.
• As 899 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 899 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:

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 numbers as 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 899 is prime or composite.

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

Step 2: Divide 899 by 2. It is not divisible by 2, so 2 is not a factor of 899.

Step 3: Divide 899 by 3. It is not divisible by 3, so 3 is not a factor of 899.

Step 4: You can simplify checking divisors by finding the square root of 899 (approximately 29.98), and then check divisors up to that value.

Step 5: When we divide 899 by 29, it is divisible by 29, so 29 is a factor of 899.

Since 899 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 9. Since 9 is not even, 899 is not divisible by 2.

Divisibility by 3: The sum of the digits in the number 899 is 26. Since 26 is not divisible by 3, 899 is also not divisible by 3.

Divisibility by 5: The unit’s place digit is 9. Therefore, 899 is not divisible by 5.

Divisibility by 7: Using the divisibility rule for 7, 899 is not divisible by 7.

Divisibility by 11: The alternating sum of the digits is 8 - 9 + 9 = 8. Since 8 is not divisible by 11, 899 is not divisible by 11.

Since 899 is divisible by 29 and 31, 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 in a systematic way, such as 1 to 1000.

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 with subsequent numbers. Through this process, we will have a list of prime numbers.

899 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 899 as 29 × 31.

Step 2: Both 29 and 31 are prime numbers.

Step 3: Now we get the product consisting of only prime numbers.

Hence, the prime factorization of 899 is 29 × 31.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 899 is a composite number because it is divisible by 1, 29, 31, and 899.

• Prime numbers: Numbers greater than 1 with only two factors, 1 and itself, are called prime numbers. For example, 29 is a prime number.

• Divisibility Test: A method to determine if a number is divisible by another without performing division. For example, a number is divisible by 2 if it ends in an even digit.

• Prime Factorization: The process of expressing a number as the product of its prime factors. For instance, the prime factorization of 60 is 2 × 2 × 3 × 5.

• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer. It systematically eliminates the multiples of each prime number starting from 2.