Last updated on May 26th, 2025
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 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.
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 !
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.
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.
— 289 is not a prime number.
— The prime factorization of 289 is 17×17.
— Factors of 289 are 1,17 and 289.
— 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.
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.
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.
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.
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.
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.
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.
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.
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.
: She loves to read number jokes and games.