Divisors of 729: All 7 Factors

Divisors (Factors) Calculator

Use the calculator above to find all divisors (also called factors) of any positive integer up to 4,782,969. Beyond the divisor list, this tool also shows divisor pairs, the sum and count of divisors, prime factorization, and number properties (prime, perfect square, perfect number).

All Divisors of 729

The number 729 has 7 divisors:

1,  3,  9,  27,  81,  243,  729

Divisor Pairs of 729

Each pair multiplies to 729:

Note: the last pair has identical factors (27 × 27) because 729 is a perfect square.

Number of Divisors

The number 729 has 7 divisors, written as τ(729) = 7 in number theory.

⚡ Notice: 729 has an odd number of divisors — this means 729 is a perfect square (√729 = 27).

Sum of Divisors

σ(729) = 1 + 3 + 9 + 27 + 81 + 243 + 729 = 1093

Prime Factorization of 729

See the full prime factorization calculator →

Properties of 729

• 729 is composite.
• 729 is a perfect square (√729 = 27).
• Number of divisors: 7.
• Sum of divisors: 1093.

Common Divisors with Another Number?

Looking for the divisors that 729 shares with another number? Use our Greatest Common Factor (GCF) calculator — it finds all common divisors and the largest one.

Step-by-Step: How to Find the Divisors of 729

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √729 ≈ 27.00. If i divides 729, then both i and 729/i are divisors.

1. 1 divides 729 (729 ÷ 1 = 729) → pair (1, 729)
2. 3 divides 729 (729 ÷ 3 = 243) → pair (3, 243)
3. 9 divides 729 (729 ÷ 9 = 81) → pair (9, 81)
4. 27 divides 729 (729 ÷ 27 = 27) → pair (27, 27)
5. Collect all unique values: {1, 3, 9, 27, 81, 243, 729} — total 7 divisors.
6. Sum: 1 + 3 + 9 + 27 + 81 + 243 + 729 = 1093.

Nearby Examples

Related Operations for 729

• Multiples of 729 — "outward" complement; M is a multiple of 729 ⇔ 729 is a divisor of M
• 729 Prime Factorization — decompose into prime building blocks
• Find GCF of 729 and another number
• Find LCM of 729 and another number
• Is 729 a perfect square? (odd divisor count ⇔ yes)

See also our tables of divisors:

• Table of all divisors from 1 to 100
• Table of all divisors from 1 to 500
• Table of all divisors from 1 to 1,000
• Table of all divisors from 1 to 10,000

What Is a Divisor?

A divisor (also called a factor) of a positive integer n is any positive integer d such that n ÷ d has no remainder. In other words, d divides n evenly.

Every positive integer n has at least two divisors: 1 and n itself (with 1 being the trivial case of having only itself). Numbers with exactly 2 divisors are prime; numbers with 3 or more divisors are composite.

Why use this calculator? Beyond just listing divisors, this tool computes the sum σ(n), the count τ(n), prime factorization, divisor pairs (useful for visual learners and factoring problems), and detects whether n is a prime, a perfect square, or a perfect number.

References

• [1] Divisor (Wikipedia)
• [2] Divisor function (Wikipedia)
• [3] Divisor (Wolfram MathWorld)

Divisors Calculation Examples

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