Divisors of 40320: All 96 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 40320

The number 40320 has 96 divisors:

1,  2,  3,  4,  5,  6,  7,  8,  9,  10,  12,  14,  15,  16,  18,  20,  21,  24,  28,  30,  32,  35,  36,  40,  42,  45,  48,  56,  60,  63,  64,  70,  72,  80,  84,  90,  96,  105,  112,  120,  126,  128,  140,  144,  160,  168,  180,  192,  210,  224,  240,  252,  280,  288,  315,  320,  336,  360,  384,  420,  448,  480,  504,  560,  576,  630,  640,  672,  720,  840,  896,  960,  1008,  1120,  1152,  1260,  1344,  1440,  1680,  1920,  2016,  2240,  2520,  2688,  2880,  3360,  4032,  4480,  5040,  5760,  6720,  8064,  10080,  13440,  20160,  40320

Divisor Pairs of 40320

Each pair multiplies to 40320:

Number of Divisors

The number 40320 has 96 divisors, written as τ(40320) = 96 in number theory.

Sum of Divisors

σ(40320) = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 12 + 14 + 15 + 16 + 18 + 20 + 21 + 24 + 28 + 30 + 32 + 35 + 36 + 40 + 42 + 45 + 48 + 56 + 60 + 63 + 64 + 70 + 72 + 80 + 84 + 90 + 96 + 105 + 112 + 120 + 126 + 128 + 140 + 144 + 160 + 168 + 180 + 192 + 210 + 224 + 240 + 252 + 280 + 288 + 315 + 320 + 336 + 360 + 384 + 420 + 448 + 480 + 504 + 560 + 576 + 630 + 640 + 672 + 720 + 840 + 896 + 960 + 1008 + 1120 + 1152 + 1260 + 1344 + 1440 + 1680 + 1920 + 2016 + 2240 + 2520 + 2688 + 2880 + 3360 + 4032 + 4480 + 5040 + 5760 + 6720 + 8064 + 10080 + 13440 + 20160 + 40320 = 159120

Prime Factorization of 40320

See the full prime factorization calculator →

Properties of 40320

• 40320 is composite.
• 40320 is not a perfect square.
• Number of divisors: 96.
• Sum of divisors: 159120.

Common Divisors with Another Number?

Looking for the divisors that 40320 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 40320

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √40320 ≈ 200.80. If i divides 40320, then both i and 40320/i are divisors.

1. 1 divides 40320 (40320 ÷ 1 = 40320) → pair (1, 40320)
2. 2 divides 40320 (40320 ÷ 2 = 20160) → pair (2, 20160)
3. 3 divides 40320 (40320 ÷ 3 = 13440) → pair (3, 13440)
4. 4 divides 40320 (40320 ÷ 4 = 10080) → pair (4, 10080)
5. 5 divides 40320 (40320 ÷ 5 = 8064) → pair (5, 8064)
6. 6 divides 40320 (40320 ÷ 6 = 6720) → pair (6, 6720)
7. 7 divides 40320 (40320 ÷ 7 = 5760) → pair (7, 5760)
8. 8 divides 40320 (40320 ÷ 8 = 5040) → pair (8, 5040)
9. 9 divides 40320 (40320 ÷ 9 = 4480) → pair (9, 4480)
10. 10 divides 40320 (40320 ÷ 10 = 4032) → pair (10, 4032)
11. 12 divides 40320 (40320 ÷ 12 = 3360) → pair (12, 3360)
12. 14 divides 40320 (40320 ÷ 14 = 2880) → pair (14, 2880)
13. 15 divides 40320 (40320 ÷ 15 = 2688) → pair (15, 2688)
14. 16 divides 40320 (40320 ÷ 16 = 2520) → pair (16, 2520)
15. 18 divides 40320 (40320 ÷ 18 = 2240) → pair (18, 2240)
16. 20 divides 40320 (40320 ÷ 20 = 2016) → pair (20, 2016)
17. 21 divides 40320 (40320 ÷ 21 = 1920) → pair (21, 1920)
18. 24 divides 40320 (40320 ÷ 24 = 1680) → pair (24, 1680)
19. 28 divides 40320 (40320 ÷ 28 = 1440) → pair (28, 1440)
20. 30 divides 40320 (40320 ÷ 30 = 1344) → pair (30, 1344)
21. 32 divides 40320 (40320 ÷ 32 = 1260) → pair (32, 1260)
22. 35 divides 40320 (40320 ÷ 35 = 1152) → pair (35, 1152)
23. 36 divides 40320 (40320 ÷ 36 = 1120) → pair (36, 1120)
24. 40 divides 40320 (40320 ÷ 40 = 1008) → pair (40, 1008)
25. 42 divides 40320 (40320 ÷ 42 = 960) → pair (42, 960)
26. 45 divides 40320 (40320 ÷ 45 = 896) → pair (45, 896)
27. 48 divides 40320 (40320 ÷ 48 = 840) → pair (48, 840)
28. 56 divides 40320 (40320 ÷ 56 = 720) → pair (56, 720)
29. 60 divides 40320 (40320 ÷ 60 = 672) → pair (60, 672)
30. 63 divides 40320 (40320 ÷ 63 = 640) → pair (63, 640)
31. 64 divides 40320 (40320 ÷ 64 = 630) → pair (64, 630)
32. 70 divides 40320 (40320 ÷ 70 = 576) → pair (70, 576)
33. 72 divides 40320 (40320 ÷ 72 = 560) → pair (72, 560)
34. 80 divides 40320 (40320 ÷ 80 = 504) → pair (80, 504)
35. 84 divides 40320 (40320 ÷ 84 = 480) → pair (84, 480)
36. 90 divides 40320 (40320 ÷ 90 = 448) → pair (90, 448)
37. 96 divides 40320 (40320 ÷ 96 = 420) → pair (96, 420)
38. 105 divides 40320 (40320 ÷ 105 = 384) → pair (105, 384)
39. 112 divides 40320 (40320 ÷ 112 = 360) → pair (112, 360)
40. 120 divides 40320 (40320 ÷ 120 = 336) → pair (120, 336)
41. 126 divides 40320 (40320 ÷ 126 = 320) → pair (126, 320)
42. 128 divides 40320 (40320 ÷ 128 = 315) → pair (128, 315)
43. 140 divides 40320 (40320 ÷ 140 = 288) → pair (140, 288)
44. 144 divides 40320 (40320 ÷ 144 = 280) → pair (144, 280)
45. 160 divides 40320 (40320 ÷ 160 = 252) → pair (160, 252)
46. 168 divides 40320 (40320 ÷ 168 = 240) → pair (168, 240)
47. 180 divides 40320 (40320 ÷ 180 = 224) → pair (180, 224)
48. 192 divides 40320 (40320 ÷ 192 = 210) → pair (192, 210)
49. Collect all unique values: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 32, 35, 36, 40, 42, 45, 48, 56, 60, 63, 64, 70, 72, 80, 84, 90, 96, 105, 112, 120, 126, 128, 140, 144, 160, 168, 180, 192, 210, 224, 240, 252, 280, 288, 315, 320, 336, 360, 384, 420, 448, 480, 504, 560, 576, 630, 640, 672, 720, 840, 896, 960, 1008, 1120, 1152, 1260, 1344, 1440, 1680, 1920, 2016, 2240, 2520, 2688, 2880, 3360, 4032, 4480, 5040, 5760, 6720, 8064, 10080, 13440, 20160, 40320} — total 96 divisors.
50. Sum: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 12 + 14 + 15 + 16 + 18 + 20 + 21 + 24 + 28 + 30 + 32 + 35 + 36 + 40 + 42 + 45 + 48 + 56 + 60 + 63 + 64 + 70 + 72 + 80 + 84 + 90 + 96 + 105 + 112 + 120 + 126 + 128 + 140 + 144 + 160 + 168 + 180 + 192 + 210 + 224 + 240 + 252 + 280 + 288 + 315 + 320 + 336 + 360 + 384 + 420 + 448 + 480 + 504 + 560 + 576 + 630 + 640 + 672 + 720 + 840 + 896 + 960 + 1008 + 1120 + 1152 + 1260 + 1344 + 1440 + 1680 + 1920 + 2016 + 2240 + 2520 + 2688 + 2880 + 3360 + 4032 + 4480 + 5040 + 5760 + 6720 + 8064 + 10080 + 13440 + 20160 + 40320 = 159120.

Nearby Examples

Related Operations for 40320

• Multiples of a Number — "outward" complement of divisors
• 40320 Prime Factorization — decompose into prime building blocks
• Find GCF of 40320 and another number
• Find LCM of 40320 and another number
• Is 40320 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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