Is 898 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 898 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 898 has more than two factors, it is not 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 898 is prime or composite.

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

Step 2: Divide 898 by 2. It is divisible by 2, so 2 is a factor of 898.

Step 3: You can simplify checking divisors up to 898 by finding the square root value. We then need to only check divisors up to the square root value, which is approximately 29.93.

Step 4: When we divide 898 by 2, 449, and other numbers up to 29, we find more than two divisors.

Since 898 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 8. Eight is an even number, which means that 898 is divisible by 2. 

Divisibility by 3: The sum of the digits in the number 898 is 25. Since 25 is not divisible by 3, 898 is also not divisible by 3. 

Divisibility by 5: The unit’s place digit is 8. Therefore, 898 is not divisible by 5. 

Divisibility by 7: The last digit in 898 is 8. To check divisibility by 7, double the last digit (8 × 2 = 16). Then, subtract it from the rest of the number (89 - 16 = 73). Since 73 is not divisible by 7, 898 is also not divisible by 7. 

Divisibility by 11: In 898, the sum of the digits in odd positions is 16, and the sum of the digits in even positions is 9. The difference is 7, which means 898 is not divisible by 11.

Since 898 is divisible by 2, 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 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.

Using this process, we can identify 898 is not 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 898 as 2 × 449.

Step 2: In 2 × 449, both 2 and 449 are prime numbers.

Hence, the prime factorization of 898 is 2 × 449.

• Prime numbers: Natural numbers greater than 1 that have only two factors, 1 and the number itself, are called prime numbers. For example, 13 is a prime number because it is divisible only by 1 and 13.

• 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.

• Divisibility rules: A set of rules that help determine if a number is divisible by another without performing division.

• Prime factorization: The process of expressing a composite number as the product of its prime factors.

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