# Factors of 1089

Factors of 1089 are 1, 3, 9, 11, 33, 99, 121, 363, and 1089

#### How to find factors of a number

 1.   Find factors of 1089 using Division Method 2.   Find factors of 1089 using Prime Factorization 3.   Find factors of 1089 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 1089

• Divide 1089 by 1: 1089 ÷ 1 : Remainder = 0
• Divide 1089 by 3: 1089 ÷ 3 : Remainder = 0
• Divide 1089 by 9: 1089 ÷ 9 : Remainder = 0
• Divide 1089 by 11: 1089 ÷ 11 : Remainder = 0
• Divide 1089 by 33: 1089 ÷ 33 : Remainder = 0
• Divide 1089 by 99: 1089 ÷ 99 : Remainder = 0
• Divide 1089 by 121: 1089 ÷ 121 : Remainder = 0
• Divide 1089 by 363: 1089 ÷ 363 : Remainder = 0
• Divide 1089 by 1089: 1089 ÷ 1089 : Remainder = 0

Hence, Factors of 1089 are 1, 3, 9, 11, 33, 99, 121, 363, and 1089

#### 2. Steps to find factors of 1089 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 1089 using the division method, follow these steps:

• Step 1. Start dividing 1089 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 1089, which is 3. Divide 1089 by 3 to obtain the quotient (363).
1089 ÷ 3 = 363
• Step 3. Repeat step 1 with the obtained quotient (363).
363 ÷ 3 = 121
121 ÷ 11 = 11
11 ÷ 11 = 1

So, the prime factorization of 1089 is, 1089 = 3 x 3 x 11 x 11.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 1089 as shown below:

So, the prime factorization of 1089 is, 1089 = 3 x 3 x 11 x 11.

#### 3. Find factors of 1089 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 1089 would be the two numbers which, when multiplied, give 1089 as the result.

The following table represents the calculation of factors of 1089 in pairs:

Factor Pair Pair Factorization
1 and 1089 1 x 1089 = 1089
3 and 363 3 x 363 = 1089
9 and 121 9 x 121 = 1089
11 and 99 11 x 99 = 1089
33 and 33 33 x 33 = 1089

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 1089. They are called negative pair factors.

Hence, the negative pairs of 1089 would be ( -1 , -1089 ) , ( -3 , -363 ) , ( -9 , -121 ) , ( -11 , -99 ) and ( -33 , -33 ) .

#### 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, 3, 9, 11, 33, 99, 121, 363, 1089 are exact divisors of 1089.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 1089 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 1089.

• Which is the smallest prime factor of 1089?

Smallest prime factor of 1089 is 3.

• Is 1089 a perfect square?

Yes 1089 is a perfect square.

• What are five multiples of 1089?

First five multiples of 1089 are 2178, 3267, 4356, 5445, 6534.

• What is prime factorization of 1089?

Prime factorization of 1089 is 3 x 3 x 11 x 11.

• What are factors of 1089?

Factors of 1089 are 1, 3, 9, 11, 33, 99, 121, 363, 1089.

• How do you find factors of a negative number? ( eg. -1089 )?

Factors of -1089 are -1, -3, -9, -11, -33, -99, -121, -363, -1089.

• Is 1089 a whole number?

Yes 1089 is a whole number.

• Which is greatest factor of 1089?

The greatest factor of 1089 is 363.

• What are the prime factors of 1089?

The factors of 1089 are 1, 3, 9, 11, 33, 99, 121, 363, 1089.
Prime factors of 1089 are 3, 3, 11, 11.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 1089. Can you help her?

Prime factors of 1089 are 3, 3, 11, 11.
Hence, the product of prime factors of 33.

Can you help Rubel to find out the product of the even factors of 1089?

Factors of 1089 are 1, 3, 9, 11, 33, 99, 121, 363, 1089.
Even factors of 1089 are 0.
Hence, product of even factors of 1089 is; 0 = 0.

Joy wants to calculate mean of all the factors of 1089. Help him in finding the mean of 1089.

Factors of 1089 are 1, 3, 9, 11, 33, 99, 121, 363, 1089.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 1089 is 1 + 3 + 9 + 11 + 33 + 99 + 121 + 363 + 1089 = 1729.
Hence, the mean of factors of 1089 is 1729 ÷ 9 = 192.11.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 1089? Help her in writing all the factors.

Positive factors are 1, 3, 9, 11, 33, 99, 121, 363, 1089.
Negative factors are -1, -3, -9, -11, -33, -99, -121, -363, -1089.

How many factors are there for 1089?

Factors of 1089 are 1, 3, 9, 11, 33, 99, 121, 363, 1089.
So there are in total 9 factors.

Joey wants to write all the prime factors of 1089 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 1089 are 3, 3, 11, 11.
So in exponential form it can be written as 32 x 112.

Kevin has been asked to write 8 factor(s) of 1089. Can you predict the answer?

8 factor(s) of 1089 are 1, 3, 9, 11, 33, 99, 121, 363.