Is 10001 a prime number?

The number 10001 has got several factors, that are capable of dividing the number completely without leaving any remainder. Thus, the number 10001 is a non-prime number. The factors of 10001 include 1, 73, 137, and 10001.

A number to be a prime number should follow the criteria, which is that it should not have factors more than 2. Here, 10001 has more than 2 factors, hence making it a composite 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, it is to be checked whether the number is divisible by any numbers other than 1 and the number itself.

The counting divisors method for 10001 would simply be:

Divisors of 10001 = 1, 73, 137, 10001
Number of divisors = 4

The number 10001 can be considered composite.

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

In the divisibility method, the prime number only has 2 divisors, which are 1 and itself.

The divisors of 10001 are 1, 73, 137, and 10001.

Thus, 10001 consists of 4 factors that divide it completely without any remainder.

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

The list of prime numbers under 100 are;
2, 3, 5, 7, 11, 13, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

10001 is not present in the list, it is not a prime number.

This method is only used for a non-prime number/composite number. Since 10001 is a composite number, the prime factorization for 10001 is:

Factors of 10001 = 73 × 137

Prime Number: A number that has exactly two distinct positive divisors: 1 and itself. For example, 2, 3, and 5 are prime numbers. Prime numbers cannot be divided by any other number without leaving a remainder.

Composite Number: A number that has more than two divisors. These numbers can be factored into smaller integers other than 1 and itself. 10001 is a composite number because it has divisors other than 1 and 10001.

Divisors: Numbers that divide another number exactly, leaving no remainder. For 10001, the divisors are 1, 73, 137, and 10001.

Prime Factorization: The process of determining the prime numbers that multiply together to give a particular number. The prime factorization of 10001 is 73 × 137.

Divisibility Test: A method used to determine whether a number is divisible by another number without leaving a remainder. The divisibility test helps identify if a number is prime or composite by checking if it can be divided by smaller numbers, such as primes.