Is 906 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 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 906 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 906 has more than two factors, it is not 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 906 is prime or composite.

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

Step 2: Divide 906 by 2. It is divisible by 2, so 2 is a factor of 906.

Step 3: Divide 906 by 3. It is divisible by 3, so 3 is a factor of 906.

Step 4: You can simplify checking divisors up to 906 by finding the root value. We then need to only check divisors up to the root value.

Step 5: Continue dividing by numbers such as 5, 7, etc., until you've checked possible factors.

Since 906 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 6. Since 6 is even, 906 is divisible by 2. -

Divisibility by 3: The sum of the digits in the number 906 is 15. Since 15 is divisible by 3, 906 is also divisible by 3. -

Divisibility by 5: The unit’s place digit is 6. Therefore, 906 is not divisible by 5. -

Divisibility by 7: There is a method for checking divisibility by 7, which involves doubling the last digit and subtracting it from the rest of the number. This can be complex for larger numbers. -

Divisibility by 11: Applying the alternating sum method does not result in a number divisible by 11, so 906 is not divisible by 11.

Since 906 is divisible by 2 and 3, among others, 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.

Through this process, we will have a list of prime numbers up to 1000. 906 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 906 as 2 × 453.

Step 2: In 453, further break it down into 3 × 151.

Step 3: 151 is a prime number. Hence, the prime factorization of 906 is 2 × 3 × 151.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 906 is a composite number because it is divisible by 1, 2, 3, 151, and itself.

• Divisibility rules: Rules used to determine whether one number is divisible by another without performing division.

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

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

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