Is 17 a prime number?
2026-02-28 13:28 Diff

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Last updated on August 5, 2025

Prime numbers are numbers with 1 and the number itself as its factor, which helps in simplifying arithmetic problems. This article will let us learn how to check for a prime number.

Is 17 a Prime Number

Numbers can be of two types, prime and composite. For the numbers to be identified as prime, it should have two factors. Number 17 only has two factors which are 1 and 17, making it a prime.
 

Why is 17 a prime number?

For a number to be identified as prime, it should satisfy the following two requirements:
A number is a factor of only 2 numbers


A number should have only two divisors, 1 and the number itself.


If the given numbers satisfy the above-mentioned conditions, then it falls into the category of prime numbers.

The methods to see if a number is prime or not are:

  • Counting Divisors Method
  • Divisibility Test Method
  • Prime Number Chart
  • Prime Factorization 
     

Using the Counting Divisors Method

 The divisors of the given number will be listed to check if it meets the conditions of a prime number.


Factors of 17= 1, 17


17 has only two factors, it is a prime 
 

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Using the Divisibility Test Method

Divisibility Method


In this method, the total number of divisors is counted to see if a number is prime.


Divisors of 17 = 1 and 17


Number of divisors = 2
 

Using Prime Number Chart

The list of prime numbers up to 20 are 1, 2, 3, 5, 7, 11, 13, 17 and 19. 


From this, we can say that 17 is a prime number.
 

Prime Factorization

In this method, we break a number into its prime factors. In the case of 17, it cannot be factored into any prime numbers. Therefore, we conclude that 17 is a prime number
 

Common mistakes to avoid when determining if 17 is a prime number

Below are few mistakes one may make when trying to determine if a number is prime. Avoid these.

FAQs : Is 17 a prime number?

1.What is a factor of 17?

Factors of 17 are numbers that completely divide 17. The factors of 17 are 1 and 17.
 

2.Are 17 and 23 prime numbers?

Yes, 17 and 23 are prime numbers because they have only two factors each. The factors of 17 are 1 and 17. The factors of 23 are 1 and 23.
 

3.Is 17 divisible?

Yes, 17 is divisible by two numbers. They are 1 and 17 itself, making it a prime number.
 

4.Is 51 divisible by 17?

Yes, 51 is completely divisible by 17. When 51 is divided by 17, we get 3 as the quotient. Here 3 and 17 are the factors of 51

5.Are twin prime numbers infinite?

Yes, the pairs of twin prime numbers are infinite. 
 

Important Glossaries for “Is 17 a prime number?”

  • Quotient: Number we get when one number is divided by another.
  • Prime numbers: A number which has only two divisors, that to be 1 and the other is the number itself.
  • Prime Factorization: In simple terms, prime factorization is a process of writing all numbers as a product of prime.
  • Composite numbers: In mathematics, composite numbers are numbers that should have more than two factors, which is 1 and itself.
     

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