Is 9 a Prime Number?

There are many tests to find if 9 is a prime number or not. But since 9 is a small number, it is easy to test. We can see that 9 has 3 divisors: 1, 3 and 9. But a prime number has only 2. So, 9 cannot be a prime number.

There are methods that can prove why 9 is not a prime number. Let us look at these methods and learn it step by step.

One of the easiest methods to find if a number is prime or not is by counting the divisors. We will list all the divisors the given number has. If the number has more than 2 divisors, it is a composite number. As we can see, 9 has three divisors. Therefore, 9 cannot be a prime number.
 

We will be checking the divisibility of 9 by a set of numbers. If divisible by any of the numbers, 9 is not a prime number.

• Divisibility by 2: For a number to be divisible by 2, it has to be an even number. But 9 is not an even number. Hence, it is not divisible by 2. 
• Divisibility by 3: The number should be a multiple of 3 to be divisible by 3. Likewise, we can see that 9 is a multiple of 3 when we multiply 3 × 3. This shows that 9 is divisible by 3
• Divisibility by 5: 9 is not divisible by 5 as it does not end with 0 or 5.
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This shows that 9 is divisible by 3, apart from 1 and 9. Since this violates the rules of a prime number, 9 is not a prime number.
 

First let us look at the prime numbers from 1 to 100: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 and 97. As we can see, 9 does not appear in the list. This confirms that 9 is not a prime number.

Prime factorization helps determine the prime factors of numbers. For instance, 9 is a composite number because it has a prime factor of 3. Indeed, 9 can be presented as 3 × 3 = 9, and thus showing it has factors other than 1 and 9.
 

• Prime Factorization: Prime factorization is one of the operations of a mathematical expression in which a number is expressed as the product of its prime factors. For example, the prime factorization of 6 is 2×3.

• Multiple:  It is the number when multiplied to another number, so multiple is the product of two numbers. Like 9, 18, 27, 36, 45 are the multiples of 9.

• Composite numbers: Composite numbers are natural numbers that are greater than 1 and have more than 2 factors other than 1 and itself. Some example for composite numbers are 4, 6 and 9.

• Whole Numbers: If a number is an integer, and it has no fraction, then it is called a whole number. Some examples for whole numbers are 1, 2, 3, 4, 5 and so on.