Is 3001 a prime number?

The number 3001 has 4 factors, which are capable of dividing the number completely without leaving any remainder. Thus, the number 3001 is a non-prime number. The factors of 3001 include 1, 7, 429, and 3001.

For a number to be a prime number, it must have no more than 2 factors: 1 and itself. Here, 3001 has more than 2 factors, hence it is classified as 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 checked whether the number is divisible by any numbers other than 1 and itself.
The counting divisors method for 3001 would simply be:

Divisors of 3001 = 1, 7, 429, 3001
Number of divisors = 4

The number 3001 can be considered composite.
 

In the divisibility 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: 1 and itself.

The divisors of 3001 are 1, 7, 429, and 3001.

Thus, 3001 consists of 4 factors that divide it completely without any remainder.
 

The prime number chart is a 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.

3001 is not present in the list, and it is not a prime number

This method is only used for a non-prime number or composite number. Since 3001 is a composite number, the prime factorization for 3001 is:

Factors of 3001 = 7 × 429
 

• 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 distinct positive divisors. For example, 4, 6, and 3001 are composite numbers.

• Divisor: A number that divides another number completely without leaving a remainder. For example, the divisors of 3001 are 1, 7, 429, and 3001.

• Prime Factorization: The expression of a composite number as a product of prime numbers. For 3001, the prime factorization is 43 × 67.

• Divisibility Test: A method used to determine whether a number can be divided by another number without a remainder. For example, using divisibility rules, 3001 is divisible by 43 and 67, making it a composite number.