Is 1859 a prime number?

The number 1859 has got 6 factors that can divide it completely without leaving any remainder. Thus, the number 1859 is a non-prime number. The factors of 1859 include 1, 11, 13, 143, 169, and 1859.

For a number to be classified as a prime number must follow the criterion of having exactly two factors: 1 and itself. Since 1859 has more than 2 factors, it is a composite number.

Below are a few methods that can be used to determine whether a number is prime or composite.

The different methods 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
    

In this method, it is checked whether the number is divisible by any numbers other than 1 and the number itself.
For 1859, the counting divisors method would be:

Divisors of 1859 = 1, 11, 13, 143, 169, 1859
Number of divisors = 6

Since the number 1859 has more than 2 divisors, it is considered a composite number.
 

In the divisibility test, we try dividing the number by smaller prime numbers to check if it is divisible. If it is divisible, it is composite; otherwise, it is prime.

For 1859, the divisors are 1, 11, 13, 143, 169, and 1859

Since 1859 has more than 2 divisors, it is not a prime number.
 

The prime number chart lists prime numbers starting from 2 to infinity.

The prime numbers from 1800 to 1900 include:
1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889

1859 is not present in this list, so it is not a prime number
 

This method is used only for composite numbers. Since 1859 is composite, its prime factorization is:

Factors of 1859 = 13 × 11 × 13

Further breaking down 143: 143= 11 × 13

So, the prime factorization of 1859 is: 13 × 11 × 13.
 

• Prime Number: A natural number greater than 1 has only two distinct divisors: 1 and itself. Examples include 2, 3, and 5.

• Composite Number: A number greater than 1 has more than two divisors. For example, in 1859, it have divisors such as 1, 11, 13, 143, 169, and 1859.

• Divisors: Numbers that can divide a given number exactly without leaving a remainder. For 1859, its divisors are 1, 11, 13, 143, 169, and 1859.

• Prime Factorization: The process of breaking down a composite number into its prime factors. For 1859, the prime factorization is 13 × 11 × 13.

• Divisibility Test: A method to check if a number can be divided by smaller prime numbers without a remainder. This test is used to determine whether a number is prime or composite.