Is 10201 a prime number?

The number 10201 has more than 2 factors that are capable of dividing the number completely without leaving any remainder. Thus, 10201 is a non-prime number. The factors of 10201 include 1, 101, and 10201.

For a number to be prime, it must have exactly 2 factors: 1 and itself. Since 10201 has 3 factors, it cannot be classified as a prime number, making it a composite number.

Below are a few methods to determine if a number is prime or composite:

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

In the counting divisors method, we check if the number is divisible by any numbers other than 1 and itself.
The counting divisors method for 10201 is as follows:

Divisors of 10201 = 1, 101, 10201
Number of divisors = 3

Since 10201 has more than 2 divisors, it is a composite number.
 

In this method, we divide the number by smaller prime numbers. If the number is divisible by any of these, it is not prime.

In the case of 10201, the number is divisible by 101, which makes it a composite number

The prime number chart lists prime numbers starting from 2 to infinity.

Prime numbers under 200 include:

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, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199.

Since 10201 is not in the list and is divisible by 101, it is not a prime number.
 

This method is used to find the prime factors of a composite number.
For 10201:

Factors of 10201 = 101×101
Prime factorization of 10201= 1012

Thus, 10201 is a composite number.
 

• Prime Number: A natural number greater than 1 with exactly two distinct positive divisors: 1 and itself. Examples include 2, 3, and 5.

• Composite Number: A natural number greater than 1 that has more than two distinct positive divisors. For example, 4, 6, and 10201 are composite numbers.

• Factors: Numbers that divide a given number exactly, leaving no remainder. For 10201, the factors are 1, 101, and 10201.

• Divisibility Test: A method to check whether a number can be divided by another number without leaving a remainder. This helps determine if a number is prime or composite.

• Prime Factorization: Expressing a number as the product of its prime factors. For example, 10201 = 101×101.