Divisors of 13689: All 15 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 13689

The number 13689 has 15 divisors:

1,  3,  9,  13,  27,  39,  81,  117,  169,  351,  507,  1053,  1521,  4563,  13689

Divisor Pairs of 13689

Each pair multiplies to 13689:

Note: the last pair has identical factors (117 × 117) because 13689 is a perfect square.

Number of Divisors

The number 13689 has 15 divisors, written as τ(13689) = 15 in number theory.

⚡ Notice: 13689 has an odd number of divisors — this means 13689 is a perfect square (√13689 = 117).

Sum of Divisors

σ(13689) = 1 + 3 + 9 + 13 + 27 + 39 + 81 + 117 + 169 + 351 + 507 + 1053 + 1521 + 4563 + 13689 = 22143

Prime Factorization of 13689

See the full prime factorization calculator →

Properties of 13689

• 13689 is composite.
• 13689 is a perfect square (√13689 = 117).
• Number of divisors: 15.
• Sum of divisors: 22143.

Common Divisors with Another Number?

Looking for the divisors that 13689 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 13689

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √13689 ≈ 117.00. If i divides 13689, then both i and 13689/i are divisors.

1. 1 divides 13689 (13689 ÷ 1 = 13689) → pair (1, 13689)
2. 3 divides 13689 (13689 ÷ 3 = 4563) → pair (3, 4563)
3. 9 divides 13689 (13689 ÷ 9 = 1521) → pair (9, 1521)
4. 13 divides 13689 (13689 ÷ 13 = 1053) → pair (13, 1053)
5. 27 divides 13689 (13689 ÷ 27 = 507) → pair (27, 507)
6. 39 divides 13689 (13689 ÷ 39 = 351) → pair (39, 351)
7. 81 divides 13689 (13689 ÷ 81 = 169) → pair (81, 169)
8. 117 divides 13689 (13689 ÷ 117 = 117) → pair (117, 117)
9. Collect all unique values: {1, 3, 9, 13, 27, 39, 81, 117, 169, 351, 507, 1053, 1521, 4563, 13689} — total 15 divisors.
10. Sum: 1 + 3 + 9 + 13 + 27 + 39 + 81 + 117 + 169 + 351 + 507 + 1053 + 1521 + 4563 + 13689 = 22143.

Nearby Examples

Related Operations for 13689

• Multiples of a Number — "outward" complement of divisors
• 13689 Prime Factorization — decompose into prime building blocks
• Find GCF of 13689 and another number
• Find LCM of 13689 and another number
• Is 13689 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)

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