Factors of 289

2. Steps to find factors of 289 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

Method 1: Division Method

To find the primefactors of 289 using the division method, follow these steps:

• Step 1. Start dividing 289 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
• Step 2. After finding the smallest prime factor of the number 289, which is 17. Divide 289 by 17 to obtain the quotient (17).
  289 ÷ 17 = 17
• Step 3. Repeat step 1 with the obtained quotient (17).
  17 ÷ 17 = 1

So, the prime factorization of 289 is, 289 = 17 x 17.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 289 as shown below:

So, the prime factorization of 289 is, 289 = 17 x 17.

3. Find factors of 289 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 289 would be the two numbers which, when multiplied, give 289 as the result.

The following table represents the calculation of factors of 289 in pairs:

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 289. They are called negative pair factors.

Hence, the negative pairs of 289 would be ( -1 , -289 ) , ( -17 , -17 ) .

How can we define factors?

In mathematics, a factor is a number which divides into another number exactly, without leaving any remainder. A factor of a number can be positive of negative.

Properties of factors

• Every factor of a number is an exact divisor of that number, example 1, 17, 289 are exact divisors of 289.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 289 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 289.

Frequently Asked Questions

• What are the prime factors of 289?

  The factors of 289 are 1, 17, 289.
  Prime factors of 289 are 17, 17.

• What is the sum of all factors of 289?

  The sum of all factors of 289 is 307.

• What are the pair factors of 289?

  Pair factors of 289 are (1,289), (17,17).

• What two numbers make 289?

  Two numbers that make 289 are 17 and 17.

• What are multiples of 289?

  First five multiples of 289 are 578, 867, 1156, 1445.

• Is 289 a perfect square?

  Yes 289 is a perfect square.

• Which is greatest factor of 289?

  The greatest factor of 289 is 17.

• How do you factors of 289?

  Factors of 289 are 1, 17, 289.

• What are five multiples of 289?

  First five multiples of 289 are 578, 867, 1156, 1445, 1734.

Examples of Factors