Factors of 729

How to find the factors of 729

Test every whole number from 1 up to the square root of 729 (√729 ≈ 27.000). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 729 ÷ 1 = 729 — so 1 and 729 are factors
• 729 ÷ 2 = 364.5 — not a whole number
• 729 ÷ 3 = 243 — so 3 and 243 are factors
• 729 ÷ 4 = 182.25 — not a whole number
• 729 ÷ 5 = 145.8 — not a whole number
• 729 ÷ 6 = 121.5 — not a whole number
• 729 ÷ 7 = 104.143 — not a whole number
• 729 ÷ 8 = 91.125 — not a whole number
• 729 ÷ 9 = 81 — so 9 and 81 are factors
• 729 ÷ 10 = 72.9 — not a whole number
• 729 ÷ 11 = 66.273 — not a whole number
• 729 ÷ 12 = 60.75 — not a whole number
• 729 ÷ 13 = 56.077 — not a whole number
• 729 ÷ 14 = 52.071 — not a whole number
• 729 ÷ 15 = 48.6 — not a whole number
• 729 ÷ 16 = 45.563 — not a whole number
• 729 ÷ 17 = 42.882 — not a whole number
• 729 ÷ 18 = 40.5 — not a whole number
• 729 ÷ 19 = 38.368 — not a whole number
• 729 ÷ 20 = 36.45 — not a whole number
• 729 ÷ 21 = 34.714 — not a whole number
• 729 ÷ 22 = 33.136 — not a whole number
• 729 ÷ 23 = 31.696 — not a whole number
• 729 ÷ 24 = 30.375 — not a whole number
• 729 ÷ 25 = 29.16 — not a whole number
• 729 ÷ 26 = 28.038 — not a whole number
• 729 ÷ 27 = 27 — so 27 and 27 are factors

Collecting both numbers from every successful division gives the complete list: 1, 3, 9, 27, 81, 243 and 729.

Prime factorization of 729

Divide by the smallest prime that fits, and keep going until the quotient is 1:

The primes you divided by give 729 = 3⁶. From the exponents you can also count the factors without listing them: (6 + 1) = 7.

Properties of 729

• 729 is a composite number.
• The sum of all its factors is 1,093; the sum of its proper factors (excluding 729) is 364, which makes it a deficient number (its proper factors add up to less than itself).
• 729 is a perfect square: 27 × 27. Perfect squares always have an odd number of factors.
• 729 is also a perfect cube: 9³.
• Multiples of 729 include 1,458, 2,187, 2,916, 3,645 and so on.

Factors vs. multiples

Factors of 729 are the numbers that divide into it; multiples of 729 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.