Divisors of 36960: 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 36960

The number 36960 has 96 divisors:

1,  2,  3,  4,  5,  6,  7,  8,  10,  11,  12,  14,  15,  16,  20,  21,  22,  24,  28,  30,  32,  33,  35,  40,  42,  44,  48,  55,  56,  60,  66,  70,  77,  80,  84,  88,  96,  105,  110,  112,  120,  132,  140,  154,  160,  165,  168,  176,  210,  220,  224,  231,  240,  264,  280,  308,  330,  336,  352,  385,  420,  440,  462,  480,  528,  560,  616,  660,  672,  770,  840,  880,  924,  1056,  1120,  1155,  1232,  1320,  1540,  1680,  1760,  1848,  2310,  2464,  2640,  3080,  3360,  3696,  4620,  5280,  6160,  7392,  9240,  12320,  18480,  36960

Divisor Pairs of 36960

Each pair multiplies to 36960:

Number of Divisors

The number 36960 has 96 divisors, written as τ(36960) = 96 in number theory.

Sum of Divisors

σ(36960) = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 10 + 11 + 12 + 14 + 15 + 16 + 20 + 21 + 22 + 24 + 28 + 30 + 32 + 33 + 35 + 40 + 42 + 44 + 48 + 55 + 56 + 60 + 66 + 70 + 77 + 80 + 84 + 88 + 96 + 105 + 110 + 112 + 120 + 132 + 140 + 154 + 160 + 165 + 168 + 176 + 210 + 220 + 224 + 231 + 240 + 264 + 280 + 308 + 330 + 336 + 352 + 385 + 420 + 440 + 462 + 480 + 528 + 560 + 616 + 660 + 672 + 770 + 840 + 880 + 924 + 1056 + 1120 + 1155 + 1232 + 1320 + 1540 + 1680 + 1760 + 1848 + 2310 + 2464 + 2640 + 3080 + 3360 + 3696 + 4620 + 5280 + 6160 + 7392 + 9240 + 12320 + 18480 + 36960 = 145152

Prime Factorization of 36960

See the full prime factorization calculator →

Properties of 36960

• 36960 is composite.
• 36960 is not a perfect square.
• Number of divisors: 96.
• Sum of divisors: 145152.

Common Divisors with Another Number?

Looking for the divisors that 36960 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 36960

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √36960 ≈ 192.25. If i divides 36960, then both i and 36960/i are divisors.

1. 1 divides 36960 (36960 ÷ 1 = 36960) → pair (1, 36960)
2. 2 divides 36960 (36960 ÷ 2 = 18480) → pair (2, 18480)
3. 3 divides 36960 (36960 ÷ 3 = 12320) → pair (3, 12320)
4. 4 divides 36960 (36960 ÷ 4 = 9240) → pair (4, 9240)
5. 5 divides 36960 (36960 ÷ 5 = 7392) → pair (5, 7392)
6. 6 divides 36960 (36960 ÷ 6 = 6160) → pair (6, 6160)
7. 7 divides 36960 (36960 ÷ 7 = 5280) → pair (7, 5280)
8. 8 divides 36960 (36960 ÷ 8 = 4620) → pair (8, 4620)
9. 10 divides 36960 (36960 ÷ 10 = 3696) → pair (10, 3696)
10. 11 divides 36960 (36960 ÷ 11 = 3360) → pair (11, 3360)
11. 12 divides 36960 (36960 ÷ 12 = 3080) → pair (12, 3080)
12. 14 divides 36960 (36960 ÷ 14 = 2640) → pair (14, 2640)
13. 15 divides 36960 (36960 ÷ 15 = 2464) → pair (15, 2464)
14. 16 divides 36960 (36960 ÷ 16 = 2310) → pair (16, 2310)
15. 20 divides 36960 (36960 ÷ 20 = 1848) → pair (20, 1848)
16. 21 divides 36960 (36960 ÷ 21 = 1760) → pair (21, 1760)
17. 22 divides 36960 (36960 ÷ 22 = 1680) → pair (22, 1680)
18. 24 divides 36960 (36960 ÷ 24 = 1540) → pair (24, 1540)
19. 28 divides 36960 (36960 ÷ 28 = 1320) → pair (28, 1320)
20. 30 divides 36960 (36960 ÷ 30 = 1232) → pair (30, 1232)
21. 32 divides 36960 (36960 ÷ 32 = 1155) → pair (32, 1155)
22. 33 divides 36960 (36960 ÷ 33 = 1120) → pair (33, 1120)
23. 35 divides 36960 (36960 ÷ 35 = 1056) → pair (35, 1056)
24. 40 divides 36960 (36960 ÷ 40 = 924) → pair (40, 924)
25. 42 divides 36960 (36960 ÷ 42 = 880) → pair (42, 880)
26. 44 divides 36960 (36960 ÷ 44 = 840) → pair (44, 840)
27. 48 divides 36960 (36960 ÷ 48 = 770) → pair (48, 770)
28. 55 divides 36960 (36960 ÷ 55 = 672) → pair (55, 672)
29. 56 divides 36960 (36960 ÷ 56 = 660) → pair (56, 660)
30. 60 divides 36960 (36960 ÷ 60 = 616) → pair (60, 616)
31. 66 divides 36960 (36960 ÷ 66 = 560) → pair (66, 560)
32. 70 divides 36960 (36960 ÷ 70 = 528) → pair (70, 528)
33. 77 divides 36960 (36960 ÷ 77 = 480) → pair (77, 480)
34. 80 divides 36960 (36960 ÷ 80 = 462) → pair (80, 462)
35. 84 divides 36960 (36960 ÷ 84 = 440) → pair (84, 440)
36. 88 divides 36960 (36960 ÷ 88 = 420) → pair (88, 420)
37. 96 divides 36960 (36960 ÷ 96 = 385) → pair (96, 385)
38. 105 divides 36960 (36960 ÷ 105 = 352) → pair (105, 352)
39. 110 divides 36960 (36960 ÷ 110 = 336) → pair (110, 336)
40. 112 divides 36960 (36960 ÷ 112 = 330) → pair (112, 330)
41. 120 divides 36960 (36960 ÷ 120 = 308) → pair (120, 308)
42. 132 divides 36960 (36960 ÷ 132 = 280) → pair (132, 280)
43. 140 divides 36960 (36960 ÷ 140 = 264) → pair (140, 264)
44. 154 divides 36960 (36960 ÷ 154 = 240) → pair (154, 240)
45. 160 divides 36960 (36960 ÷ 160 = 231) → pair (160, 231)
46. 165 divides 36960 (36960 ÷ 165 = 224) → pair (165, 224)
47. 168 divides 36960 (36960 ÷ 168 = 220) → pair (168, 220)
48. 176 divides 36960 (36960 ÷ 176 = 210) → pair (176, 210)
49. Collect all unique values: {1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 14, 15, 16, 20, 21, 22, 24, 28, 30, 32, 33, 35, 40, 42, 44, 48, 55, 56, 60, 66, 70, 77, 80, 84, 88, 96, 105, 110, 112, 120, 132, 140, 154, 160, 165, 168, 176, 210, 220, 224, 231, 240, 264, 280, 308, 330, 336, 352, 385, 420, 440, 462, 480, 528, 560, 616, 660, 672, 770, 840, 880, 924, 1056, 1120, 1155, 1232, 1320, 1540, 1680, 1760, 1848, 2310, 2464, 2640, 3080, 3360, 3696, 4620, 5280, 6160, 7392, 9240, 12320, 18480, 36960} — total 96 divisors.
50. Sum: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 10 + 11 + 12 + 14 + 15 + 16 + 20 + 21 + 22 + 24 + 28 + 30 + 32 + 33 + 35 + 40 + 42 + 44 + 48 + 55 + 56 + 60 + 66 + 70 + 77 + 80 + 84 + 88 + 96 + 105 + 110 + 112 + 120 + 132 + 140 + 154 + 160 + 165 + 168 + 176 + 210 + 220 + 224 + 231 + 240 + 264 + 280 + 308 + 330 + 336 + 352 + 385 + 420 + 440 + 462 + 480 + 528 + 560 + 616 + 660 + 672 + 770 + 840 + 880 + 924 + 1056 + 1120 + 1155 + 1232 + 1320 + 1540 + 1680 + 1760 + 1848 + 2310 + 2464 + 2640 + 3080 + 3360 + 3696 + 4620 + 5280 + 6160 + 7392 + 9240 + 12320 + 18480 + 36960 = 145152.

Nearby Examples

Related Operations for 36960

• Multiples of a Number — "outward" complement of divisors
• 36960 Prime Factorization — decompose into prime building blocks
• Find GCF of 36960 and another number
• Find LCM of 36960 and another number
• Is 36960 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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