Is 1729 a prime number?

The number 1729 has got multiple factors, which are capable of dividing the number completely without leaving any remainder. Thus, the number 1729 is a non-prime number. The factors of 1729 include 1, 7, 13, 17, 91, 119, 221, and 1729.

A number to be a prime number should follow the criteria, which is that it should not have factors more than 2. Here, 1729 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 1729 would simply be

Divisors of 1729 = 1, 7, 13, 17, 91, 119, 221, 1729
Number of divisors = 8

The number 1729 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 1729 are 1, 7, 13, 17, 91, 119, 221, and 1729.

Thus, 1729 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.

1729 is not present in the list, so it is not a prime number.

This method is only used for a non-prime number/composite number. Since 1729 is a composite number, the prime factorization for 1729 is:

Factors of 1729 = 7 × 13 × 19

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 positive integer greater than 1 that has more than two distinct positive divisors. Unlike prime numbers, composite numbers can be divided by factors other than 1 and themselves. Example: 1729 is a composite number.

Divisors: The numbers that can divide a given number completely without leaving a remainder. For 1729, its divisors are 1, 7, 13, 17, 91, 119, 221, and 1729.

Prime Factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 1729 is 7×13×197 \times 13 \times 197×13×19.

Divisibility Test: A method used to check if a number is divisible by another. If a number is divisible by a prime number, it is not a prime number itself. For 1729, divisibility tests show that it is divisible by 7, 13, and 17, indicating it is not prime.