Factor Calculator

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.

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Factor pairs of 81

These 3 pairs of whole numbers each multiply to give 81.

1 × 81 = 81
3 × 27 = 81
9 × 9 = 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:

81 ÷ 3 = 27
27 ÷ 3 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1
Result: 81 = 3 × 3 × 3 × 3 = 3⁴

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.

Factor tree of 81813273933
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 81

Number of factors5
Sum of factors121
Sum of proper factors40
Prime factorization3⁴
Prime or composite?Composite
Even or odd?Odd
Perfect square?Yes (9²)
Perfect cube?No
ClassificationDeficient

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 √819.00, because every factor above that pairs with one below it.

81 ÷ 1 = 81
81 ÷ 3 = 27
81 ÷ 9 = 9

Reading both columns gives every factor: 1, 3, 9, 27, 81. The factor calculator does this automatically for any number.

Frequently asked questions about 81

What are the factors of 81?

The factors of 81 are 1, 3, 9, 27, and 81. That is 5 factors in total, counting both 1 and 81.

Is 81 a prime number?

No, 81 is not prime — it is a composite number with 5 factors. A prime number has exactly two factors, but 81 is also divisible by 3.

What is the prime factorization of 81?

The prime factorization of 81 is 3⁴. Written out in full: 3 × 3 × 3 × 3 = 81. Its distinct prime factors are 3.

What two numbers multiply to give 81?

There are 3 pairs of whole numbers that multiply to 81: 1 × 81, 3 × 27, 9 × 9.

What is the sum of the factors of 81?

Adding all the factors of 81 together gives 121. Excluding 81 itself, the proper factors sum to 40.

Is 81 a perfect square?

Yes, 81 is a perfect square. It equals 9 × 9. Perfect squares always have an odd number of factors — 81 has 5.

What is the largest factor of 81 other than itself?

The largest factor of 81 apart from 81 itself is 27, since 81 ÷ 27 = 3.

How many factors does 81 have?

81 has 5 factors: 1, 3, 9, 27, and 81. You can verify this from the prime factorization 3⁴: add 1 to each exponent and multiply, giving 5 = 5.

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.