Is 10011 a prime number?

The number 10011 has more than 2 factors, meaning it is capable of being divided completely by multiple numbers without leaving a remainder. Thus, the number 10011 is a non-prime number. The factors of 10011 include 1, 3, 3337, and 10011.

A number to be a prime number should follow the criteria that it should not have factors more than 2. Here, 10011 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 10011 would simply be:

Divisors of 10011 = 1, 3, 3337, 10011
Number of divisors = 4

The number 10011 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 10011 are 1, 3, 3337, and 10011.

Thus, 10011 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, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

10011 is not present in the list of smaller prime numbers, nor is it prime based on the divisibility test.
 

This method is only used for a non-prime number/composite number. Since 10011 is a composite number, the prime factorization for 10011 is:

Factors of 10011 = 3 × 3337
 

• Prime Number: A natural number greater than 1 that has only two distinct positive divisors: 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 distinct positive divisors. For example, 4, 6, and 10011 are composite numbers, as they have factors other than 1 and the number itself.

• Divisibility Test: A method used to determine if one number can be evenly divided by another number, without leaving a remainder. For example, checking if 10011 is divisible by prime numbers like 3, 5, or 7.

• Prime Factorization: The process of breaking down a composite number into the product of prime numbers. For 10011, the prime factorization is 3 × 73 × 47.

• Counting Divisors Method: A technique for finding all divisors of a number by listing every number that divides it evenly. For 10011, the divisors are 1, 3, 3337, and 10011, showing it is not prime.