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Last updated on May 26th, 2025

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Factors of 289

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Factors are the ‘building blocks’ of a number. They are the numbers that can be multiplied together to reach the number you started with. 289 is an interesting number. It is large enough to make you think, but simple enough to learn if you know a few tricks. Let’s dive into it!

Factors of 289 for Qatari Students
Professor Greenline from BrightChamps

What are the factors of 289?

Factors are whole numbers that, when multiplied, the product is equal to 289. 


289 is not a prime number, its factors are 1,17 and 289. For every factor, there is a corresponding negative factor, for 289, the negative factors -1, -17 and -289.

Professor Greenline from BrightChamps

How to find the factors of 289?

There are various methods we apply to find the factors of any number. Few of them are listed here;  multiplication method, division method, prime factors and prime factorization and factor tree method. These are explained in detail below, let’s learn !
 

Professor Greenline from BrightChamps

Finding Factors Using Multiplication

Step 1: Find all pairs of numbers whose product is 289. 


Step 2: All the pairs found represent the factors of 289. 


289 is not a prime number. The pair of numbers whose product is 289 is;


1×289=289 


17×17 = 289


The factors of 289 are 1,17 and 289.
 

Professor Greenline from BrightChamps

Finding Factors by Division Method

Step 1: Start by dividing 289 with the smallest number, and check the remainders. 


Step 2: 289 is not prime, therefore the divisors it has are 1,17 and 289. Any number that is further checked for divisibility leaves behind a remainder.


The factors of 289 are 1,17 and 289.
 

Professor Greenline from BrightChamps

Prime factors and prime factorization

— 289 is not a prime number.


— The prime factorization of 289 is 17×17.


— Factors of 289 are 1,17 and 289.
 

Professor Greenline from BrightChamps

Factor tree

— In this method, we make branches that extend from the number to express a number as the product of its factors. 


— In the case of 289, only one branch will be extended, as the number is prime factorized as 17×17. 17 is a prime number and cannot be factored further. 
 

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Common mistakes and how to avoid them in the factors of 289

We all make mistakes when it comes to finding factors, especially when it comes to numbers like 289. Don’t worry, it is a part of learning. Here are a few common slip-ups we may make, along with tips to avoid them. 
 

Mistake 1

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Excluding negative factors 
 

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 Every positive factor has a corresponding negative factor. Often times, the negative factors are not included. 
 

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Factors of 289 Examples

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Max, the Girl Character from BrightChamps

Problem 1

Given that one factor of 289 is 17, find the other factor.

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We know that 17×?=289


Divide 289 by 17: 289÷17=17


So, the other factor is 17.
 

Explanation

Since 289 is 17×17, if one factor is 17, the other must also be 17. This is a useful approach when you know one factor but need to find the other.
 

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Max, the Girl Character from BrightChamps

Problem 2

Verify that 289 is a perfect square by using its factors.

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We know that 289 can be written as 17×17.


Since 289 is the result of a number multiplied by itself, it is a perfect square.


Therefore, 289 is a perfect square, and its square root is 17.
 

Explanation

A perfect square is a number that can be expressed as a product of an integer with itself. Since 289 is 17×17, it meets this requirement, confirming that it’s a perfect square.
 

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Max, the Girl Character from BrightChamps

Problem 3

Is 289 divisible by 13?

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Divide 289 by 13: 289÷13=22.23


Since 22.23 is not a whole number, 13 is not a factor of 289.
 

Explanation

To check divisibility, divide 289 by 13. If the result is a whole number, 13 would be a factor. Since 13 does not divide 289 evenly, it’s not a factor.
 

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FAQs on Factors of 289

1.What are the two roots of 289?

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2.Is 289 a natural number?

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3. Is 289 odd or even?

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4.Is 289 a perfect square?

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5.Is the cube root of 289 rational?

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6.How can children in Qatar use numbers in everyday life to understand Factors of 289?

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7.What are some fun ways kids in Qatar can practice Factors of 289 with numbers?

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8.What role do numbers and Factors of 289 play in helping children in Qatar develop problem-solving skills?

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9.How can families in Qatar create number-rich environments to improve Factors of 289 skills?

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Professor Greenline from BrightChamps

Important Glossaries for Factors of 289

  • Factors: numbers that divide the given number without leaving a remainder. 

 

  • Prime factorization: breaking numbers down into their prime factors.

 

  • Prime factors: Prime numbers that multiply together to form a given number.

 

  • Composite number: Number that has at least more than one divisor other than 1 and the number itself.
Professor Greenline from BrightChamps

About BrightChamps in Qatar

At BrightChamps, numbers are more than symbols—they open pathways to countless chances! Our mission is to help kids throughout Qatar master important math skills, focusing today on Factors of 289 with special attention to factors—in an engaging, clear, and fun way. Whether your child is figuring out the speed of a ride at Angry Birds World, tracking local football scores, or managing their allowance for gadgets, strong number skills boost their confidence for daily tasks. Our interactive lessons make learning straightforward and enjoyable. Since kids in Qatar learn uniquely, we customize lessons to each child’s needs. From Doha’s modern cityscape to desert surroundings, BrightChamps brings math to life across Qatar. Let’s make factors an exciting part of every child’s math journey!
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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.

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Fun Fact

: She loves to read number jokes and games.

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