Is 100001 a prime number?

The number 100001 has got 4 factors, that are capable of dividing the number completely without leaving any remainder. Thus, the number 100001 is a non-prime number. The factors of 100001 include 1, 41, 2431, and 100001.

A number to be a prime number should follow the criteria, which is that it should not have factors more than 2. Here, 100001 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 100001 would simply be:

Divisors of 100001 = 1, 41, 2431, 100001
Number of divisors = 4

The number 100001 can be considered composite.
 

In the division test, 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 100001 are 1, 41, 2431, and 100001.

Thus, 100001 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.

100001 is not present in the list, so we need to check larger numbers.

Upon further investigation, it is divisible by 41 and 2431, indicating it is not a prime number.
 

This method is only used for a non-prime number/composite number. Since 100001 is a composite number, the prime factorization for 100001 is:

Factors of 100001 = 41 × 2431
 

• Prime Number: A natural number greater than 1 that has no positive divisors other than 1 and itself. For example, 2, 3, 5, and 7 are prime numbers.

• Composite Number: A natural number greater than 1 that has more than two divisors, meaning it can be divided by numbers other than 1 and itself. For example, 100001 is a composite number because it has divisors like 41 and 2431.

• Divisibility: The ability of one number to be divided by another without leaving a remainder. If a number divides another evenly, it is said to divide it completely.

• Prime Factorization: The expression of a composite number as a product of prime numbers. For example, the prime factorization of 100001 is 11 × 9091.

• Divisors: Numbers that divide another number exactly, without leaving a remainder. For 100001, the divisors are 1, 41, 2431, and 100001.