Is 123123 a prime number?

The number 123123 has multiple factors that are capable of dividing the number completely without leaving any remainder. Thus, the number 123123 is a non-prime number. The factors of 123123 include 1, 3, 7, 9, 21, 27, 49, 63, 147, 189, 343, 567, 1029, 2049, 4913, 8199, 14739, 34317, and 123123.

A number to be a prime number should follow the criteria, which is that it should not have factors more than 2. Here, 123123 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 123123 would simply be:

Divisors of 123123 = 1, 3, 7, 9, 21, 27, 49, 63, 147, 189, 343, 567, 1029, 2049, 4913, 8199, 14739, 34317, 123123
Number of divisors = 19

The number 123123 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 123123 are 1, 3, 7, 9, 21, 27, 49, 63, 147, 189, 343, 567, 1029, 2049, 4913, 8199, 14739, 34317, 123123.

Thus, 123123 consists of 19 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.

123123 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 123123 is a composite number, the prime factorization for 123123 is:

Factors of 123123 = 3 × 7 × 9 × 49 × 63
 

• Prime Number: A natural number greater than 1 that has only two divisors: 1 and itself. Numbers such as 2, 3, and 5 are prime numbers.

• Divisibility: The ability of one number to be divided by another number without leaving a remainder. For example, 123123 is divisible by 3 because 123123 ÷ 3 results in an integer.

• Composite Number: A positive integer greater than 1 that has more than two divisors. For example, 123123 is a composite number because it has multiple divisors.

• Prime Factorization: Breaking down a composite number into the prime numbers that multiply to give the original number. The prime factorization of 123123 is 3 × 7 × 13 × 293.

• Divisor: A number that divides another number exactly without leaving a remainder. For example, the divisors of 123123 include 1, 3, 7, 13, and others.