Is 908 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 908 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 908 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers: -

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 908 is prime or composite.

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

Step 2: Divide 908 by 2. It is divisible by 2, so 2 is a factor of 908.

Step 3: Divide 908 by 3. It is not divisible by 3, so 3 is not a factor of 908.

Step 4: You can simplify checking divisors up to 908 by finding the square root value. We then need to only check divisors up to the square root value.

Step 5: When we divide 908 by 2, 4, and other numbers, it is divisible by 2, 4, 227, and 454.

Since 908 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, which is an even number, meaning that 908 is divisible by 2. 

Divisibility by 3: The sum of the digits in the number 908 is 17. Since 17 is not divisible by 3, 908 is not divisible by 3. 

Divisibility by 5: The unit’s place digit is 8, so 908 is not divisible by 5. 

Divisibility by 7: When applying the rule, 908 is not divisible by 7. -

Divisibility by 11: The alternating sum of the digits of 908 gives 1, which is not divisible by 11.

Since 908 is divisible by 2 and 4, 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 complete the table consisting of marked and crossed boxes, except 1.

Through this process, we will have a list of prime numbers from 1 to 1000. 908 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 908 as 2 × 454.

Step 2: In 2 × 454, 454 is a composite number. Further, break down 454 into 2 × 227.

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

Hence, the prime factorization of 908 is 2 × 2 × 227.

• 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 numbers: Numbers greater than 1 that have no divisors other than 1 and themselves.

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

• Prime factorization: Breaking down a number into its basic prime number building blocks.

• Co-prime numbers: Two numbers that have no common factors other than 1.