Is 9001 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, 8 is divisible by 1, 2, 4, and 8, making it a composite number.

Prime numbers follow several properties such as:

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 9001 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 9001 has more than two factors, it is not a prime number. Several methods are used to distinguish between prime and composite numbers. A few methods are:

• Counting Divisors Method
  
   
• Divisibility Test
  
   
• Prime Number Chart
  
   
• 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 9001 is prime or composite.

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

Step 2: Divide 9001 by small prime numbers like 2, 3, 5, 7, etc., up to its square root.

Step 3: 9001 is not divisible by 2 (as it is odd), 3 (since the sum of digits 9+0+0+1=10 is not divisible by 3), or 5 (as it does not end in 0 or 5).

Step 4: Continue checking until a factor is found. 9001 is divisible by 73 (9001 ÷ 73 = 123).

Since 9001 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: 9001 is odd, so it is not divisible by 2.

Divisibility by 3: The sum of the digits in the number 9001 is 10, which is not divisible by 3, so 9001 is not divisible by 3.

Divisibility by 5: The unit’s place digit is 1, so 9001 is not divisible by 5.

Divisibility by 7: Dividing 9001 by 7 does not yield a whole number, so it is not divisible by 7.

The tests show that 9001 is divisible by 73, confirming it is composite.

The prime number chart is a tool created using a method called “The Sieve of Eratosthenes.” In this method, we follow these steps:

Step 1: Write numbers starting from 1 onwards in rows and columns until beyond 9001.

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 all numbers are checked.

9001 would not appear in the list of prime numbers because it is divisible by 73, making it composite.

Prime factorization is a process of breaking down a number into prime factors and then multiplying those factors to obtain the original number.

Step 1: Start with the smallest prime number, which is 2, and check divisibility.

Step 2: 9001 is not divisible by 2, 3, or 5.

Step 3: Continue testing prime numbers until divisibility is found.

Step 4: 9001 = 73 × 123.

Since 123 is also composite, further breakdown may be needed.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 9001 is a composite number because it is divisible by 73 and 123.
  
   
• Prime factorization: The process of expressing a number as the product of its prime factors.
  
   
• Divisibility rules: Techniques used to determine if one number is divisible by another without performing division.
  
   
• Odd numbers: Numbers that are not divisible by 2. Most prime numbers are odd, but not all odd numbers are prime.
  
   
• Square root: A value that, when multiplied by itself, gives the original number. It is used to simplify the process of finding factors.