Factors of 1089
The factors of 1089 are 1, 3, 9, 11, 33, 99, 121, 363, and 1089. In total, 1089 has 9 factors. Its prime factorization is 3² × 11², and the sum of all its factors is 1729. 1089 is also a perfect square, equal to 33 × 33.
All factors of 1089
Here are all 9 factors of 1089, listed from smallest to largest.
Factor pairs of 1089
These 5 pairs of whole numbers each multiply to give 1089.
Notice the pair (33, 33) — because 1089 is a perfect square, this pair uses the same number twice.
Prime factorization of 1089
Dividing 1089 by the smallest prime at each step gives its prime factorization:
The distinct prime factors of 1089 are 3, 11. To factorize any other number, use the prime factorization calculator.
Factor tree of 1089
A factor tree shows the same prime factorization visually. Each composite branch splits until every endpoint is a prime number.
Properties of 1089
| Number of factors | 9 |
|---|---|
| Sum of factors | 1729 |
| Sum of proper factors | 640 |
| Prime factorization | 3² × 11² |
| Prime or composite? | Composite |
| Even or odd? | Odd |
| Perfect square? | Yes (33²) |
| Perfect cube? | No |
| Classification | Deficient |
What makes 1089 interesting
- 1089 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 5 different ways.
- 1089 is a perfect square: 33 × 33 = 1089. This is why it has an odd number of factors (9) — the pair (33, 33) counts only once.
- 1089 is a deficient number: its proper factors sum to 640, which is 449 less than 1089 itself.
How to find the factors of 1089 yourself
Divide 1089 by each whole number starting from 1. Whenever the division leaves no remainder, both the divisor and the quotient are factors. You only need to test up to √1089 ≈ 33.00, because every factor above that pairs with one below it.
Reading both columns gives every factor: 1, 3, 9, 11, 33, 99, 121, 363, 1089. The factor calculator does this automatically for any number.
Related numbers
Numbers mathematically connected to 1089.
Frequently asked questions about 1089
What are the factors of 1089?
Is 1089 a prime number?
What is the prime factorization of 1089?
What two numbers multiply to give 1089?
What is the sum of the factors of 1089?
Is 1089 a perfect square?
What is the largest factor of 1089 other than itself?
How many factors does 1089 have?
Explore more
Try another number in the factor calculator, break 1089 down further with the prime factorization calculator, or compare 1089 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.