Factor Calculator

Factors of 810

The factors of 810 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 270, 405, and 810. In total, 810 has 20 factors. Its prime factorization is 2 × 3⁴ × 5, and the sum of all its factors is 2178.

All factors of 810

Here are all 20 factors of 810, listed from smallest to largest.

123569101518273045548190135162270405810

Factor pairs of 810

These 10 pairs of whole numbers each multiply to give 810.

1 × 810 = 810
2 × 405 = 810
3 × 270 = 810
5 × 162 = 810
6 × 135 = 810
9 × 90 = 810
10 × 81 = 810
15 × 54 = 810
18 × 45 = 810
27 × 30 = 810

Prime factorization of 810

Dividing 810 by the smallest prime at each step gives its prime factorization:

810 ÷ 2 = 405
405 ÷ 3 = 135
135 ÷ 3 = 45
45 ÷ 3 = 15
15 ÷ 3 = 5
5 ÷ 5 = 1
Result: 810 = 2 × 3 × 3 × 3 × 3 × 5 = 2 × 3⁴ × 5

The distinct prime factors of 810 are 2, 3, 5. To factorize any other number, use the prime factorization calculator.

Factor tree of 810

A factor tree shows the same prime factorization visually. Each composite branch splits until every endpoint is a prime number.

Factor tree of 8108102405313534531535
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 810

Number of factors20
Sum of factors2178
Sum of proper factors1368
Prime factorization2 × 3⁴ × 5
Prime or composite?Composite
Even or odd?Even
Perfect square?No
Perfect cube?No
ClassificationAbundant

What makes 810 interesting

  • 810 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 10 different ways.
  • 810 is an abundant number: its proper factors sum to 1368, which is 558 more than 810 itself.
  • 810 has 3 distinct prime factors (2, 3, 5), which is why it has so many divisors.

How to find the factors of 810 yourself

Divide 810 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 √810 ≈ 28.46, because every factor above that pairs with one below it.

810 ÷ 1 = 810 ✓
810 ÷ 2 = 405 ✓
810 ÷ 3 = 270 ✓
810 ÷ 5 = 162 ✓
810 ÷ 6 = 135 ✓
810 ÷ 9 = 90 ✓
810 ÷ 10 = 81 ✓
810 ÷ 15 = 54 ✓
810 ÷ 18 = 45 ✓
810 ÷ 27 = 30 ✓

Reading both columns gives every factor: 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 270, 405, 810. The factor calculator does this automatically for any number.

Numbers mathematically connected to 810.

Frequently asked questions about 810

What are the factors of 810?

The factors of 810 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 270, 405, and 810. That is 20 factors in total, counting both 1 and 810.

Is 810 a prime number?

No, 810 is not prime — it is a composite number with 20 factors. A prime number has exactly two factors, but 810 is also divisible by 2.

What is the prime factorization of 810?

The prime factorization of 810 is 2 × 3⁴ × 5. Written out in full: 2 × 3 × 3 × 3 × 3 × 5 = 810. Its distinct prime factors are 2, 3, 5.

What two numbers multiply to give 810?

There are 10 pairs of whole numbers that multiply to 810: 1 × 810, 2 × 405, 3 × 270, 5 × 162, 6 × 135, 9 × 90, 10 × 81, 15 × 54, 18 × 45, 27 × 30.

What is the sum of the factors of 810?

Adding all the factors of 810 together gives 2178. Excluding 810 itself, the proper factors sum to 1368.

Is 810 a perfect square?

No, 810 is not a perfect square. There is no whole number that multiplies by itself to give 810. The nearest perfect squares are 784 and 841.

What is the largest factor of 810 other than itself?

The largest factor of 810 apart from 810 itself is 405, since 810 ÷ 405 = 2.

How many factors does 810 have?

810 has 20 factors: 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 270, 405, and 810. You can verify this from the prime factorization 2 × 3⁴ × 5: add 1 to each exponent and multiply, giving 2 × 5 × 2 = 20.

Explore more

Try another number in the factor calculator, break 810 down further with the prime factorization calculator, or compare 810 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.