Is 1721 a prime number?
2026-02-28 13:59 Diff
https://brightchamps.com/en-us/math/numbers/is-1721-a-prime-number

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Last updated on August 5, 2025

Prime numbers have only 1 and the number itself as factors. They play a vital role in digital security and secure online transactions. The discussion below explores whether 1721 is a prime number and the methods used to determine it.

Is 1721 a prime number?

Why is 1721 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

Using the Counting Divisors Method

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.

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Using the Divisibility Method

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.

Using the Prime Number Chart

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.

Common mistakes to avoid when determining if 1721 is a prime number

It is highly likely we commit some mistakes due to confusion or unclear understanding. Let us look at possible mistakes we may make and try to avoid them.

FAQs for “Is 1721 a prime number?”

1.What is the largest prime factor of 1721?

Since 1721 is a prime number, its largest prime factor is 1721 itself.

2.What is the smallest prime factor of 1721?

The smallest prime factor of 1721 is 1721 because it is a prime number.

3.Is 1721 a composite number?

No, 1721 is not a composite number because it has only two factors: 1 and itself.

4.How to express 1721 as a product of prime factors?

As 1721 is a prime number, it cannot be factored further. It is expressed as 1721×1.

5.Represent 1721 in the prime factor tree?

A prime factor tree for 1721 will simply have 1721 as the only node since it is a prime number.

6.Do any perfect squares exist in the prime factors of 1721?

No, there are no perfect squares in the prime factors of 1721 as it is a prime number.

7.Do any perfect cubes exist in the prime factors of 1721?

No, there are no perfect cubes in the prime factors of 1721 since it is a prime number.

8.What can 1721 be divided by?

1721 can only be divided by 1 and 1721, as it is a prime number.

Glossary for "Is 1721 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. 

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Hiralee Lalitkumar Makwana

About the Author

Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.

Fun Fact

: She loves to read number jokes and games.