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Factors of 1089

Factors of 1089 are the list of integers that we can split evenly into 1089. There are overall 9 factors of 1089 among which 1089 is the biggest factor and 1, 3, 9, 11, 33, 99, 121, 363, 1089 are positive factors. The Prime Factors of 1089 are 3 × 11 and its Factors in Pairs are (1, 1089), (3, 363), (9, 121), (11, 99), (33, 33).

  • All Factors of 1089: 1, 3, 9, 11, 33, 99, 121, 363 and 1089
  • Negative Factors of 1089: -1, -3, -9, -11, -33, -99, -121, -363 and -1089
  • Prime Factors of 1089: 3, 11
  • Prime Factorization of 1089: 32 × 112
  • Sum of Factors of 1089: 1729
1. What Are the Factors of 1089?
2. Factors of 1089 by Prime Factorization
3. Factors of 1089 in Pairs
4. FAQs on Factors of 1089
Factors of 1089

What are Factors of 1089?

Factors of 1089 are pairs of those numbers whose products result in 1089. These factors are either prime numbers or composite numbers.

How to Find the Factors of 1089?

To find the factors of 1089, we will have to find the list of numbers that would divide 1089 without leaving any remainder.

  • 1089/11 = 99; therefore, 11 is a factor of 1089 and 99 is also a factor of 1089.
  • 1089/33 = 33; therefore, 33 is a factor of 1089.
Similarly we can find other factors. Hence, the factors of 1089 are 1, 3, 9, 11, 33, 99, 121, 363, 1089.

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Factors of 1089 by Prime Factorization

The number 1089 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 1089. The first step is to divide the number 1089 with the smallest prime factor, here it is 3. We keep dividing until it gives a non-zero remainder.
  • 1089 ÷ 3 = 363
  • 363 ÷ 3 = 121

Further dividing 121 by 3 gives a non-zero remainder. So we stop the process and continue dividing the number 121 by the next smallest prime factor. We stop ultimately if the next prime factor doesn't exist or when we can't divide any further.

So, the prime factorization of 1089 can be written as 32 × 112 where 3, 11 are prime.

 

Factors of 1089 in Pairs

Pair factors of 1089 are the pairs of numbers that when multiplied give the product 1089. The factors of 1089 in pairs are:

  • 1 × 1089 = (1, 1089)
  • 3 × 363 = (3, 363)
  • 9 × 121 = (9, 121)
  • 11 × 99 = (11, 99)
  • 33 × 33 = (33, 33)

Negative pair factors of 1089 are:

  • -1 × -1089 = (-1, -1089)
  • -3 × -363 = (-3, -363)
  • -9 × -121 = (-9, -121)
  • -11 × -99 = (-11, -99)
  • -33 × -33 = (-33, -33)

NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.

Factors of 1089 Solved Examples

  1. Example 1: How many factors are there for 1089?

    Solution:

    The factors of 1089 are too many, therefore if we can find the prime factorization of 1089, then the total number of factors can be calculated using the formula shown below.
    If the prime factorization of the number is ax × by × cz where a, b, c are prime, then the total number of factors can be given by (x + 1)(y + 1)(z + 1).

    Prime Factorization of 1089 = 32 × 112
    Therefore, the total number of factors are (2 + 1) × (2 + 1) = 3 × 3 = 9

  2. Example 2: Find the Least Common Multiple and Greatest Common Divisor (GCD) of 1089 and 548.

    Solution:

    The factors of 1089 are 1, 3, 9, 11, 33, 99, 121, 363, 1089 and factors of 548 are 1, 2, 4, 137, 274, 548.

    Therefore, the Least Common Multiple of 1089 and 548 is 596772 and Greatest Common Divisor (GCD) of 1089 and 548 is 1.

  3. Example 3: Find if 3, 9, 11, 33 and 949 are factors of 1089.

    Solution:

    When we divide 1089 by 949 it leaves a remainder. Therefore, the number 949 is not a factor of 1089. All numbers except 949 are factors of 1089.

  4. Example 4: Find the product of all the prime factors of 1089.

    Solution:

    Since, the prime factors of 1089 are 3, 11. Therefore, the product of prime factors = 3 × 11 = 33.

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FAQs on Factors of 1089

What are the Factors of 1089?

The factors of 1089 are 1, 3, 9, 11, 33, 99, 121, 363, 1089 and its negative factors are -1, -3, -9, -11, -33, -99, -121, -363, -1089.

What is the Sum of all Factors of 1089?

Sum of all factors of 1089 = (32 + 1 - 1)/(3 - 1) × (112 + 1 - 1)/(11 - 1) = 1729

What are the Pair Factors of 1089?

The pair factors of 1089 are (1, 1089), (3, 363), (9, 121), (11, 99), (33, 33).

What is the Greatest Common Factor of 1089 and 237?

The factors of 1089 and 237 are 1, 3, 9, 11, 33, 99, 121, 363, 1089 and 1, 3, 79, 237 respectively.

Common factors of 1089 and 237 are [1, 3].

Hence, the Greatest Common Factor (GCF) of 1089 and 237 is 3.

How Many Factors of 1089 are also Factors of 362?

Since, the factors of 1089 are 1, 3, 9, 11, 33, 99, 121, 363, 1089 and factors of 362 are 1, 2, 181, 362. Hence, 1089 and 362 have only one common factor which is 1. Therefore, 1089 and 362 are co-prime.

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