Is 10101 a prime number?

The number 10101 has multiple factors that divide it completely without leaving any remainder. Thus, the number 10101 is a non-prime number. The factors of 10101 include 1, 3, 37, 101, 1111, 303, 3337, and 10101.

For a number to be a prime number, it must meet the criterion of having only two factors: 1 and the number itself. Since 10101 has more than two factors, it is classified as a composite number.

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

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

In this method, we check if the number is divisible by any numbers other than 1 and the number itself.
For 10101, the divisors are:

Divisors of 10101 = 1, 3, 37, 101, 1111, 303, 3337, 10101
Number of divisors = 8

Since 10101 has more than 2 divisors, it is considered a composite number.
 

In the divisibility method, we test whether the number is divisible by any smaller prime numbers. If it is divisible, then the number is composite.

For 10101, the divisors are:

Divisors of 10101 = 1, 3, 37, 101, 1111, 303, 3337, 10101

Since it has 8 divisors, 10101 is not a prime number.
 

The prime number chart lists 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.

Since 10101 is not in this list and is divisible by 3 and other numbers, it is not a prime number.
 

Prime factorization is used for composite numbers to find their prime factors. Since 10101 is a composite number, its prime factorization is:

Factors of 10101 = 3 × 37 × 101
 

• Prime Number: A natural number greater than 1 that has exactly two distinct positive divisors: 1 and itself. For example, 2, 3, and 5 are prime numbers.

• Composite Number: A natural number greater than 1 that has more than two positive divisors. For example, 4, 6, and 9 are composite numbers.

• Divisor: A number that divides another number completely without leaving a remainder. For example, divisors of 6 are 1, 2, 3, and 6.

• Prime Factorization: The process of breaking down a composite number into the product of its prime factors. For instance, the prime factorization of 12 is 2×2×32 \times 2 \times 32×2×3.

• Divisibility Test: A method to check whether a number can be divided evenly by another number, often used to determine if a number is prime or composite. For example, a divisibility test for 3 involves checking if the sum of the digits of the number is divisible by 3.