How to find the factors of 81
Test every whole number from 1 up to the square root of 81 (√81 ≈ 9.000). Each number that divides evenly gives you two factors at once: the divisor and the quotient.
- 81 ÷ 1 = 81 — so 1 and 81 are factors
- 81 ÷ 2 = 40.5 — not a whole number
- 81 ÷ 3 = 27 — so 3 and 27 are factors
- 81 ÷ 4 = 20.25 — not a whole number
- 81 ÷ 5 = 16.2 — not a whole number
- 81 ÷ 6 = 13.5 — not a whole number
- 81 ÷ 7 = 11.571 — not a whole number
- 81 ÷ 8 = 10.125 — not a whole number
- 81 ÷ 9 = 9 — so 9 and 9 are factors
Collecting both numbers from every successful division gives the complete list: 1, 3, 9, 27 and 81.
Prime factorization of 81
Divide by the smallest prime that fits, and keep going until the quotient is 1:
The primes you divided by give 81 = 3⁴. From the exponents you can also count the factors without listing them: (4 + 1) = 5.
Properties of 81
- 81 is a composite number.
- The sum of all its factors is 121; the sum of its proper factors (excluding 81) is 40, which makes it a deficient number (its proper factors add up to less than itself).
- 81 is a perfect square: 9 × 9. Perfect squares always have an odd number of factors.
- Multiples of 81 include 162, 243, 324, 405 and so on.
Factors vs. multiples
Factors of 81 are the numbers that divide into it; multiples of 81 are the numbers it divides into. Every number has a limited set of factors but infinitely many multiples. To work with any other number, use the factors calculator, or find shared factors with the GCF calculator.
Frequently asked questions
What are the factors of 81?
The factors of 81 are 1, 3, 9, 27 and 81. Each of these divides 81 with no remainder.
How many factors does 81 have?
81 has 5 positive factors, which form 3 factor pairs. Counting negative factors as well doubles that to 10.
What is the prime factorization of 81?
81 = 3⁴. Its distinct prime factors are 3.
Is 81 a prime number?
No. 81 is composite because it has 5 factors, more than the two a prime number has.