Is 14641 a prime number?

The number 14641 has more than two factors, which means it is not a prime number. The factors of 14641 include 1, 11, 121, 14641.

A number to be a prime number should follow the criteria, which is that it should not have factors more than 2. Here, 14641 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 14641 would simply be:

Divisors of 14641 = 1, 11, 121, 14641
Number of divisors = 4

The number 14641 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 14641 are 1, 11, 121, and 14641.

Thus, 14641 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.

14641 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 14641 is a composite number, the prime factorization for 14641 is:

Factors of 14641 = 11 × 11 × 11 × 11
 

• Prime Number: A number greater than 1 that has exactly two distinct positive divisors: 1 and itself. Examples include 2, 3, and 5. 14641 is not a prime number because it has more than two divisors.

• Composite Number: A number that has more than two positive divisors, meaning it can be divided by numbers other than 1 and itself. 14641 is a composite number because it has factors 1, 11, 121, and 14641.

• Divisibility Test: A method used to determine if a number can be divided by another without leaving a remainder. In the case of 14641, it is divisible by 11, confirming it is not prime.

• Prime Factorization: Breaking down a composite number into the product of prime numbers. For 14641, the prime factorization is 11 × 11 × 11 × 11 (or 11⁴).

• Perfect Square: A number that is the square of an integer. 14641 is a perfect square because it can be expressed as 121², where 121 is a prime factor of 14641.