Is 345 a prime number?

The number 345 has got 6 factors, that are capable of dividing the number completely without leaving any remainder. Thus, the number 345 is a non-prime number. The factors of 345 include 1, 3, 5, 15, 23, 69, 115, and 345.

A number to be a prime number should follow the criteria, which is that it should not have factors more than 2. Here, 345 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 345 would simply be:

Divisors of 345 = 1, 3, 5, 15, 23, 69, 115, 345

Number of divisors = 8

The number 345 can be considered composite.
 

In the division method, 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 345 are 1, 3, 5, 15, 23, 69, 115, and 345.

Thus, 345 consists of 8 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.

345 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 345 is a composite number, the prime factorization for 345 is:

Factors of 345 = 3 × 5 × 23
 

• Prime Number: A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Example: 727 is a prime number because it can only be divided by 1 and 727.

• Divisibility: Divisibility refers to whether one number can be divided by another without leaving a remainder. For example, 727 is divisible by 1 and 727, which confirms its primality.

• Divisors: Divisors are numbers that can divide another number completely without leaving a remainder. For 727, its divisors are 1 and 727, confirming it is a prime number.

• Composite Number: A composite number is a natural number greater than 1 that has more than two divisors. Unlike prime numbers, composite numbers can be factored into smaller integers. Example: 727 is a composite number.

• Prime Factorization: Prime factorization is the process of expressing a number as a product of prime numbers. For example, the prime factorization of 727 is 7 × 103.