Divisors of 13440: All 64 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 13440

The number 13440 has 64 divisors:

1,  2,  3,  4,  5,  6,  7,  8,  10,  12,  14,  15,  16,  20,  21,  24,  28,  30,  32,  35,  40,  42,  48,  56,  60,  64,  70,  80,  84,  96,  105,  112,  120,  128,  140,  160,  168,  192,  210,  224,  240,  280,  320,  336,  384,  420,  448,  480,  560,  640,  672,  840,  896,  960,  1120,  1344,  1680,  1920,  2240,  2688,  3360,  4480,  6720,  13440

Divisor Pairs of 13440

Each pair multiplies to 13440:

Number of Divisors

The number 13440 has 64 divisors, written as τ(13440) = 64 in number theory.

Sum of Divisors

σ(13440) = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 10 + 12 + 14 + 15 + 16 + 20 + 21 + 24 + 28 + 30 + 32 + 35 + 40 + 42 + 48 + 56 + 60 + 64 + 70 + 80 + 84 + 96 + 105 + 112 + 120 + 128 + 140 + 160 + 168 + 192 + 210 + 224 + 240 + 280 + 320 + 336 + 384 + 420 + 448 + 480 + 560 + 640 + 672 + 840 + 896 + 960 + 1120 + 1344 + 1680 + 1920 + 2240 + 2688 + 3360 + 4480 + 6720 + 13440 = 48960

Prime Factorization of 13440

See the full prime factorization calculator →

Properties of 13440

• 13440 is composite.
• 13440 is not a perfect square.
• Number of divisors: 64.
• Sum of divisors: 48960.

Common Divisors with Another Number?

Looking for the divisors that 13440 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 13440

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √13440 ≈ 115.93. If i divides 13440, then both i and 13440/i are divisors.

1. 1 divides 13440 (13440 ÷ 1 = 13440) → pair (1, 13440)
2. 2 divides 13440 (13440 ÷ 2 = 6720) → pair (2, 6720)
3. 3 divides 13440 (13440 ÷ 3 = 4480) → pair (3, 4480)
4. 4 divides 13440 (13440 ÷ 4 = 3360) → pair (4, 3360)
5. 5 divides 13440 (13440 ÷ 5 = 2688) → pair (5, 2688)
6. 6 divides 13440 (13440 ÷ 6 = 2240) → pair (6, 2240)
7. 7 divides 13440 (13440 ÷ 7 = 1920) → pair (7, 1920)
8. 8 divides 13440 (13440 ÷ 8 = 1680) → pair (8, 1680)
9. 10 divides 13440 (13440 ÷ 10 = 1344) → pair (10, 1344)
10. 12 divides 13440 (13440 ÷ 12 = 1120) → pair (12, 1120)
11. 14 divides 13440 (13440 ÷ 14 = 960) → pair (14, 960)
12. 15 divides 13440 (13440 ÷ 15 = 896) → pair (15, 896)
13. 16 divides 13440 (13440 ÷ 16 = 840) → pair (16, 840)
14. 20 divides 13440 (13440 ÷ 20 = 672) → pair (20, 672)
15. 21 divides 13440 (13440 ÷ 21 = 640) → pair (21, 640)
16. 24 divides 13440 (13440 ÷ 24 = 560) → pair (24, 560)
17. 28 divides 13440 (13440 ÷ 28 = 480) → pair (28, 480)
18. 30 divides 13440 (13440 ÷ 30 = 448) → pair (30, 448)
19. 32 divides 13440 (13440 ÷ 32 = 420) → pair (32, 420)
20. 35 divides 13440 (13440 ÷ 35 = 384) → pair (35, 384)
21. 40 divides 13440 (13440 ÷ 40 = 336) → pair (40, 336)
22. 42 divides 13440 (13440 ÷ 42 = 320) → pair (42, 320)
23. 48 divides 13440 (13440 ÷ 48 = 280) → pair (48, 280)
24. 56 divides 13440 (13440 ÷ 56 = 240) → pair (56, 240)
25. 60 divides 13440 (13440 ÷ 60 = 224) → pair (60, 224)
26. 64 divides 13440 (13440 ÷ 64 = 210) → pair (64, 210)
27. 70 divides 13440 (13440 ÷ 70 = 192) → pair (70, 192)
28. 80 divides 13440 (13440 ÷ 80 = 168) → pair (80, 168)
29. 84 divides 13440 (13440 ÷ 84 = 160) → pair (84, 160)
30. 96 divides 13440 (13440 ÷ 96 = 140) → pair (96, 140)
31. 105 divides 13440 (13440 ÷ 105 = 128) → pair (105, 128)
32. 112 divides 13440 (13440 ÷ 112 = 120) → pair (112, 120)
33. Collect all unique values: {1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 32, 35, 40, 42, 48, 56, 60, 64, 70, 80, 84, 96, 105, 112, 120, 128, 140, 160, 168, 192, 210, 224, 240, 280, 320, 336, 384, 420, 448, 480, 560, 640, 672, 840, 896, 960, 1120, 1344, 1680, 1920, 2240, 2688, 3360, 4480, 6720, 13440} — total 64 divisors.
34. Sum: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 10 + 12 + 14 + 15 + 16 + 20 + 21 + 24 + 28 + 30 + 32 + 35 + 40 + 42 + 48 + 56 + 60 + 64 + 70 + 80 + 84 + 96 + 105 + 112 + 120 + 128 + 140 + 160 + 168 + 192 + 210 + 224 + 240 + 280 + 320 + 336 + 384 + 420 + 448 + 480 + 560 + 640 + 672 + 840 + 896 + 960 + 1120 + 1344 + 1680 + 1920 + 2240 + 2688 + 3360 + 4480 + 6720 + 13440 = 48960.

Nearby Examples

Related Operations for 13440

• Multiples of a Number — "outward" complement of divisors
• 13440 Prime Factorization — decompose into prime building blocks
• Find GCF of 13440 and another number
• Find LCM of 13440 and another number
• Is 13440 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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