Divisors of 13824: All 40 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 13824

The number 13824 has 40 divisors:

1,  2,  3,  4,  6,  8,  9,  12,  16,  18,  24,  27,  32,  36,  48,  54,  64,  72,  96,  108,  128,  144,  192,  216,  256,  288,  384,  432,  512,  576,  768,  864,  1152,  1536,  1728,  2304,  3456,  4608,  6912,  13824

Divisor Pairs of 13824

Each pair multiplies to 13824:

Number of Divisors

The number 13824 has 40 divisors, written as τ(13824) = 40 in number theory.

Sum of Divisors

σ(13824) = 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 16 + 18 + 24 + 27 + 32 + 36 + 48 + 54 + 64 + 72 + 96 + 108 + 128 + 144 + 192 + 216 + 256 + 288 + 384 + 432 + 512 + 576 + 768 + 864 + 1152 + 1536 + 1728 + 2304 + 3456 + 4608 + 6912 + 13824 = 40920

Prime Factorization of 13824

See the full prime factorization calculator →

Properties of 13824

• 13824 is composite.
• 13824 is not a perfect square.
• Number of divisors: 40.
• Sum of divisors: 40920.

Common Divisors with Another Number?

Looking for the divisors that 13824 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 13824

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √13824 ≈ 117.58. If i divides 13824, then both i and 13824/i are divisors.

1. 1 divides 13824 (13824 ÷ 1 = 13824) → pair (1, 13824)
2. 2 divides 13824 (13824 ÷ 2 = 6912) → pair (2, 6912)
3. 3 divides 13824 (13824 ÷ 3 = 4608) → pair (3, 4608)
4. 4 divides 13824 (13824 ÷ 4 = 3456) → pair (4, 3456)
5. 6 divides 13824 (13824 ÷ 6 = 2304) → pair (6, 2304)
6. 8 divides 13824 (13824 ÷ 8 = 1728) → pair (8, 1728)
7. 9 divides 13824 (13824 ÷ 9 = 1536) → pair (9, 1536)
8. 12 divides 13824 (13824 ÷ 12 = 1152) → pair (12, 1152)
9. 16 divides 13824 (13824 ÷ 16 = 864) → pair (16, 864)
10. 18 divides 13824 (13824 ÷ 18 = 768) → pair (18, 768)
11. 24 divides 13824 (13824 ÷ 24 = 576) → pair (24, 576)
12. 27 divides 13824 (13824 ÷ 27 = 512) → pair (27, 512)
13. 32 divides 13824 (13824 ÷ 32 = 432) → pair (32, 432)
14. 36 divides 13824 (13824 ÷ 36 = 384) → pair (36, 384)
15. 48 divides 13824 (13824 ÷ 48 = 288) → pair (48, 288)
16. 54 divides 13824 (13824 ÷ 54 = 256) → pair (54, 256)
17. 64 divides 13824 (13824 ÷ 64 = 216) → pair (64, 216)
18. 72 divides 13824 (13824 ÷ 72 = 192) → pair (72, 192)
19. 96 divides 13824 (13824 ÷ 96 = 144) → pair (96, 144)
20. 108 divides 13824 (13824 ÷ 108 = 128) → pair (108, 128)
21. Collect all unique values: {1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 128, 144, 192, 216, 256, 288, 384, 432, 512, 576, 768, 864, 1152, 1536, 1728, 2304, 3456, 4608, 6912, 13824} — total 40 divisors.
22. Sum: 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 16 + 18 + 24 + 27 + 32 + 36 + 48 + 54 + 64 + 72 + 96 + 108 + 128 + 144 + 192 + 216 + 256 + 288 + 384 + 432 + 512 + 576 + 768 + 864 + 1152 + 1536 + 1728 + 2304 + 3456 + 4608 + 6912 + 13824 = 40920.

Nearby Examples

Related Operations for 13824

• Multiples of a Number — "outward" complement of divisors
• 13824 Prime Factorization — decompose into prime building blocks
• Find GCF of 13824 and another number
• Find LCM of 13824 and another number
• Is 13824 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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