Factor Calculator

Factors of 729

The factors of 729 are 1, 3, 9, 27, 81, 243, and 729. In total, 729 has 7 factors. Its prime factorization is 3⁶, and the sum of all its factors is 1093. 729 is also a perfect square, equal to 27 × 27.

All factors of 729

Here are all 7 factors of 729, listed from smallest to largest.

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Factor pairs of 729

These 4 pairs of whole numbers each multiply to give 729.

1 × 729 = 729
3 × 243 = 729
9 × 81 = 729
27 × 27 = 729

Notice the pair (27, 27) — because 729 is a perfect square, this pair uses the same number twice.

Prime factorization of 729

Dividing 729 by the smallest prime at each step gives its prime factorization:

729 ÷ 3 = 243
243 ÷ 3 = 81
81 ÷ 3 = 27
27 ÷ 3 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1
Result: 729 = 3 × 3 × 3 × 3 × 3 × 3 = 3⁶

The distinct prime factors of 729 are 3. To factorize any other number, use the prime factorization calculator.

Factor tree of 729

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

Factor tree of 72972932433813273933
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 729

Number of factors7
Sum of factors1093
Sum of proper factors364
Prime factorization3⁶
Prime or composite?Composite
Even or odd?Odd
Perfect square?Yes (27²)
Perfect cube?Yes (9³)
ClassificationDeficient

What makes 729 interesting

  • 729 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 4 different ways.
  • 729 is a perfect square: 27 × 27 = 729. This is why it has an odd number of factors (7) — the pair (27, 27) counts only once.
  • 729 is a perfect cube: 9 × 9 × 9 = 729.
  • 729 is a deficient number: its proper factors sum to 364, which is 365 less than 729 itself.
  • 729 is a prime power: it is 3 raised to the power of 6. All of its factors are powers of 3.

How to find the factors of 729 yourself

Divide 729 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 √729 ≈ 27.00, because every factor above that pairs with one below it.

729 ÷ 1 = 729 ✓
729 ÷ 3 = 243 ✓
729 ÷ 9 = 81 ✓
729 ÷ 27 = 27 ✓

Reading both columns gives every factor: 1, 3, 9, 27, 81, 243, 729. The factor calculator does this automatically for any number.

Numbers mathematically connected to 729.

Frequently asked questions about 729

What are the factors of 729?

The factors of 729 are 1, 3, 9, 27, 81, 243, and 729. That is 7 factors in total, counting both 1 and 729.

Is 729 a prime number?

No, 729 is not prime — it is a composite number with 7 factors. A prime number has exactly two factors, but 729 is also divisible by 3.

What is the prime factorization of 729?

The prime factorization of 729 is 3⁶. Written out in full: 3 × 3 × 3 × 3 × 3 × 3 = 729. Its distinct prime factors are 3.

What two numbers multiply to give 729?

There are 4 pairs of whole numbers that multiply to 729: 1 × 729, 3 × 243, 9 × 81, 27 × 27.

What is the sum of the factors of 729?

Adding all the factors of 729 together gives 1093. Excluding 729 itself, the proper factors sum to 364.

Is 729 a perfect square?

Yes, 729 is a perfect square. It equals 27 × 27. Perfect squares always have an odd number of factors — 729 has 7.

What is the largest factor of 729 other than itself?

The largest factor of 729 apart from 729 itself is 243, since 729 ÷ 243 = 3.

How many factors does 729 have?

729 has 7 factors: 1, 3, 9, 27, 81, 243, and 729. You can verify this from the prime factorization 3⁶: add 1 to each exponent and multiply, giving 7 = 7.

Explore more

Try another number in the factor calculator, break 729 down further with the prime factorization calculator, or compare 729 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.