Factors of 81
The factors of 81 are 1, 3, 9, 27, and 81. In total, 81 has 5 factors. Its prime factorization is 3⁴, and the sum of all its factors is 121. 81 is also a perfect square, equal to 9 × 9.
All factors of 81
Here are all 5 factors of 81, listed from smallest to largest.
Factor pairs of 81
These 3 pairs of whole numbers each multiply to give 81.
Notice the pair (9, 9) — because 81 is a perfect square, this pair uses the same number twice.
Prime factorization of 81
Dividing 81 by the smallest prime at each step gives its prime factorization:
The distinct prime factors of 81 are 3. To factorize any other number, use the prime factorization calculator.
Factor tree of 81
A factor tree shows the same prime factorization visually. Each composite branch splits until every endpoint is a prime number.
Properties of 81
| Number of factors | 5 |
|---|---|
| Sum of factors | 121 |
| Sum of proper factors | 40 |
| Prime factorization | 3⁴ |
| Prime or composite? | Composite |
| Even or odd? | Odd |
| Perfect square? | Yes (9²) |
| Perfect cube? | No |
| Classification | Deficient |
What makes 81 interesting
- 81 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 3 different ways.
- 81 is a perfect square: 9 × 9 = 81. This is why it has an odd number of factors (5) — the pair (9, 9) counts only once.
- 81 is a deficient number: its proper factors sum to 40, which is 41 less than 81 itself.
- 81 is a prime power: it is 3 raised to the power of 4. All of its factors are powers of 3.
How to find the factors of 81 yourself
Divide 81 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 √81 ≈ 9.00, because every factor above that pairs with one below it.
Reading both columns gives every factor: 1, 3, 9, 27, 81. The factor calculator does this automatically for any number.
Related numbers
Numbers mathematically connected to 81.
Frequently asked questions about 81
What are the factors of 81?
Is 81 a prime number?
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What is the sum of the factors of 81?
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Explore more
Try another number in the factor calculator, break 81 down further with the prime factorization calculator, or compare 81 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.