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414 LearnersLast updated on December 11, 2025
Factors of 289
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.
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 !
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.
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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.
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.
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.
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
Excluding negative factors
Every positive factor has a corresponding negative factor. Often times, the negative factors are not included.
Mistake 2
Forgetting to include 1
1 is frequently forgotten when the factors of a number are listed, 1 is a factor of all whole numbers including primes and itself.
Mistake 3
Assuming 289 is prime
One may wrongly assume that the number 289 is prime and not look for factors. 289 is a composite number.
Factors of 289 Examples
Problem 1
Given that one factor of 289 is 17, find the other factor.
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.
Problem 2
Verify that 289 is a perfect square by using its factors.
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.
Problem 3
Is 289 divisible by 13?
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.
FAQs on Factors of 289
1.What are the two roots of 289?
2.Is 289 a natural number?
3. Is 289 odd or even?
4.Is 289 a perfect square?
5.Is the cube root of 289 rational?
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.
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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.
