289/2 = 144.5. A remainder is being left behind making the number 289 odd by nature

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Last updated on December 9th, 2024

Factors of 289

Q: What are the two roots of 289?

The two roots of 289 are 17 and -17. These numbers multiplied by themselves gives us the number 289.

Q: Is 289 a natural number?

Yes. 289 is a natural number. All numbers that range from 1 to infinity are called natural numbers. 289 falls between 288 and 230.

Q: Is 289 a perfect square?

17 multiplied by itself gives us 289. The square is a whole number making it a perfect square.

Q: Is the cube root of 289 rational?

The cube root of 289 is 6.61148901846. We cannot write 6.61148901846 in the form of p/q where q is not equal to zero, which is the condition for a number to be a rational number.

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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!

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.

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

Factors of 289 Examples

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Problem 1

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

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Explanation

Problem 2

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

Explanation

Problem 3

Is 289 divisible by 13?

Explanation

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.