Is 1721 a prime number?

The number 1721 has exactly 2 factors, 1 and 1721, which can divide the number completely without leaving any remainder. Thus, 1721 is classified as a prime number.

A number is considered a prime number if it has only 2 factors: 1 and the number itself. Since 1721 meets this criterion, it is a prime number.

Below are some commonly used methods to verify if a number is prime or composite.

Methods to check if a number is a prime number:

1. Counting Divisors Method
2. Divisibility Test
3. Prime Number Chart
4. Prime Factorization

In this method, we count the total divisors of the number.

For 1721:

Divisors of 1721 = 1, 1721
Number of divisors = 2

Since 1721 has only 2 divisors, it is a prime number.

Here, the number is tested for divisibility by smaller prime numbers (like 2, 3, 5, 7, etc.).

1721 is not divisible by any smaller prime number, confirming it has no divisors other than 1 and itself.
Thus, 1721 qualifies as a prime number.

A prime number chart lists all prime numbers starting from 2 onward.

The list of prime numbers from 1700 to 1800 are:
1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789

Since 1721 is present in this list, it is a prime number.

Prime Number: A natural number greater than 1 that has exactly two distinct positive divisors: 1 and itself. For example, 1721 is a prime number.

Divisors: Numbers that divide another number completely without leaving a remainder. For instance, the divisors of 1721 are 1 and 1721.

Composite Number: A natural number greater than 1 that has more than two distinct positive divisors. For example, 12 is a composite number because it has divisors 1, 2, 3, 4, 6, and 12.

Prime Factorization: Expressing a number as a product of its prime factors. For a prime number like 1721, the factorization is simply 1721 × 1.

Divisibility Test: A method to determine if one number can divide another number without leaving a remainder.