Factors of 289

The factors of 289 are the numbers that divide 289 evenly and leave a remainder 0. In other words, the numbers that are multiplied together in pairs resulting in 289 are the factors of 289. The factors or the pair factors of 289 can be represented in positive and negative form. For example, the pair factor of 289 is expressed as (1, 289) or (-1, -289). If we multiply -1 ad -289, it will result in the original number 289. In this article, we are going to discuss the factors of 289, positive and negative pair factors of 289, prime factors of 289 using the prime factorization method and many solved examples.

Table of Contents:

• What are the Factors of 289?
• Pair Factors of 289
• Factors of 289 by Division Method
• Prime Factorization of 289
• Solved Examples
• FAQs

What are the Factors of 289?

The numbers that divide 289 completely without leaving a remainder are called the factors of 289. As 289 is a composite number, it has more than two factors. The factors of 289 are 1, 17 and 289. Similarly, the negative factors of 289 are -1, -17 and -289.

Pair Factors of 289

The numbers that are multiplied in pairs resulting in the original number 289 are the pair factors of 289. As discussed above, the pair factors of 289 can be represented in positive as well as negative form. Thus, the positive and negative pair factors of 289 are given below:

Positive Pair Factors of 289:

Negative Pair Factors of 289:

Factors of 289 by Division Method

In the division method, the factors of 289 are found by dividing 289 by different integers. If the integers divide 289 exactly and leave a remainder 0, then those integers are the factors of 289. Now, let us start dividing 289 by 1 and continue with the different integers.

• 289/1 = 289 (Factor is 1 and Remainder is 0)
• 289/17 = 17 (Factor is 17 and Remainder is 0)
• 289/289 = 1 (Factor is 289 and Remainder is 0)

If we divide 289 by any numbers other than 1, 17 and 289, it leaves a remainder of some value. Hence, the factors of 289 are 1, 17 and 289.

Prime Factorization of 289

The process of writing the number 289 as a product of its prime factors is called the prime factorization of 289. Go through the following procedure to find the prime factors of 289.

Take a pair factor of 289, say (1, 289).

We know that the number 1 cannot be split further as it is neither prime nor composite. So, take the other number 289, which is a composite number.

Now, find the two numbers which on multiplication give the result 289.

Hence, the number 289 is written as a product of 17 and 17. Now, 17 is a prime number, which cannot be split further.

Therefore, the prime factorization of 289 is 17 × 17 or 17².

Video Lesson on Prime Factors

Solved Examples

Example 1:

Find the common factors of 289 and 145.

Solution:

The factors of 289 are 1, 17 and 289.

The factors of 145 are 1, 5, 29 and 145.

Thus, the common factor of 289 and 145 is 1.

Example 2:

What are the common factors of 289 and 287?

Solution:

Factors of 289 = 1, 17 and 289.

Factors of 287 = 1, 7, 41 and 287.

Hence, the common factor of 289 and 287 is 1 only.

Example 3:

Find the common factors of 289 and 290.

Solution:

The factors of 289 are 1, 17 and 289.

The factors of 290 are 1, 2, 5, 10, 29, 58, 145 and 290.

Therefore, the common factor of 289 and 290 is 1 only.