Is 9973 a prime number?

The number 9973 has only two factors: 1 and 9973 itself. Therefore, 9973 is a prime number.

A number is considered prime if it has no divisors other than 1 and itself. Since 9973 has only these two factors, it qualifies as a prime number.

Given below are a few ways that can be used to find prime or composite numbers.

The different methods we can use to check if a number is a prime number are explained below.

1. Counting Divisors Method
2. Divisibility Test
3. Prime Number Chart
4. Prime Factorization
    

For the counting divisors method, we check whether the number is divisible by any numbers other than 1 and the number itself.

For 9973, the divisors are:

Divisors of 9973 = 1, 9973
Number of divisors = 2

Since 9973 has only 2 divisors, it is considered a prime number.
 

In the divisibility test, we try to divide the number by any of the prime numbers. If we cannot, then it is considered a prime number.

For 9973, we check its divisibility by prime numbers up to the square root of 9973.

Since 9973 is not divisible by any prime numbers, it remains a prime number.
 

The prime number chart is a list of prime numbers starting from 2 to infinity.

Here is the list of prime numbers under 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, 97.

Since 9973 is much larger than the numbers listed above, it is not in the list under 100, but it is confirmed as a prime number after further divisibility checks.
 

• Prime Number: A natural number greater than 1 that has no divisors other than 1 and itself. Example: 9973 is a prime number because its only divisors are 1 and 9973.

• Divisibility Test: A method used to check whether a number is divisible by another number. If a number is not divisible by any primes up to its square root, it is prime.

• Divisors: Numbers that divide another number exactly without leaving a remainder. For 9973, the divisors are 1 and 9973.

• Prime Factorization: The process of breaking down a number into its prime factors. Since 9973 is prime, its prime factorization is simply 9973 itself.

• Composite Number: A number that has more than two divisors (i.e., it is divisible by numbers other than 1 and itself). 9973 is not a composite number because it is prime.