Divisors of 31680: All 84 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 31680

The number 31680 has 84 divisors:

1,  2,  3,  4,  5,  6,  8,  9,  10,  11,  12,  15,  16,  18,  20,  22,  24,  30,  32,  33,  36,  40,  44,  45,  48,  55,  60,  64,  66,  72,  80,  88,  90,  96,  99,  110,  120,  132,  144,  160,  165,  176,  180,  192,  198,  220,  240,  264,  288,  320,  330,  352,  360,  396,  440,  480,  495,  528,  576,  660,  704,  720,  792,  880,  960,  990,  1056,  1320,  1440,  1584,  1760,  1980,  2112,  2640,  2880,  3168,  3520,  3960,  5280,  6336,  7920,  10560,  15840,  31680

Divisor Pairs of 31680

Each pair multiplies to 31680:

Number of Divisors

The number 31680 has 84 divisors, written as τ(31680) = 84 in number theory.

Sum of Divisors

σ(31680) = 1 + 2 + 3 + 4 + 5 + 6 + 8 + 9 + 10 + 11 + 12 + 15 + 16 + 18 + 20 + 22 + 24 + 30 + 32 + 33 + 36 + 40 + 44 + 45 + 48 + 55 + 60 + 64 + 66 + 72 + 80 + 88 + 90 + 96 + 99 + 110 + 120 + 132 + 144 + 160 + 165 + 176 + 180 + 192 + 198 + 220 + 240 + 264 + 288 + 320 + 330 + 352 + 360 + 396 + 440 + 480 + 495 + 528 + 576 + 660 + 704 + 720 + 792 + 880 + 960 + 990 + 1056 + 1320 + 1440 + 1584 + 1760 + 1980 + 2112 + 2640 + 2880 + 3168 + 3520 + 3960 + 5280 + 6336 + 7920 + 10560 + 15840 + 31680 = 118872

Prime Factorization of 31680

See the full prime factorization calculator →

Properties of 31680

• 31680 is composite.
• 31680 is not a perfect square.
• Number of divisors: 84.
• Sum of divisors: 118872.

Common Divisors with Another Number?

Looking for the divisors that 31680 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 31680

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √31680 ≈ 177.99. If i divides 31680, then both i and 31680/i are divisors.

1. 1 divides 31680 (31680 ÷ 1 = 31680) → pair (1, 31680)
2. 2 divides 31680 (31680 ÷ 2 = 15840) → pair (2, 15840)
3. 3 divides 31680 (31680 ÷ 3 = 10560) → pair (3, 10560)
4. 4 divides 31680 (31680 ÷ 4 = 7920) → pair (4, 7920)
5. 5 divides 31680 (31680 ÷ 5 = 6336) → pair (5, 6336)
6. 6 divides 31680 (31680 ÷ 6 = 5280) → pair (6, 5280)
7. 8 divides 31680 (31680 ÷ 8 = 3960) → pair (8, 3960)
8. 9 divides 31680 (31680 ÷ 9 = 3520) → pair (9, 3520)
9. 10 divides 31680 (31680 ÷ 10 = 3168) → pair (10, 3168)
10. 11 divides 31680 (31680 ÷ 11 = 2880) → pair (11, 2880)
11. 12 divides 31680 (31680 ÷ 12 = 2640) → pair (12, 2640)
12. 15 divides 31680 (31680 ÷ 15 = 2112) → pair (15, 2112)
13. 16 divides 31680 (31680 ÷ 16 = 1980) → pair (16, 1980)
14. 18 divides 31680 (31680 ÷ 18 = 1760) → pair (18, 1760)
15. 20 divides 31680 (31680 ÷ 20 = 1584) → pair (20, 1584)
16. 22 divides 31680 (31680 ÷ 22 = 1440) → pair (22, 1440)
17. 24 divides 31680 (31680 ÷ 24 = 1320) → pair (24, 1320)
18. 30 divides 31680 (31680 ÷ 30 = 1056) → pair (30, 1056)
19. 32 divides 31680 (31680 ÷ 32 = 990) → pair (32, 990)
20. 33 divides 31680 (31680 ÷ 33 = 960) → pair (33, 960)
21. 36 divides 31680 (31680 ÷ 36 = 880) → pair (36, 880)
22. 40 divides 31680 (31680 ÷ 40 = 792) → pair (40, 792)
23. 44 divides 31680 (31680 ÷ 44 = 720) → pair (44, 720)
24. 45 divides 31680 (31680 ÷ 45 = 704) → pair (45, 704)
25. 48 divides 31680 (31680 ÷ 48 = 660) → pair (48, 660)
26. 55 divides 31680 (31680 ÷ 55 = 576) → pair (55, 576)
27. 60 divides 31680 (31680 ÷ 60 = 528) → pair (60, 528)
28. 64 divides 31680 (31680 ÷ 64 = 495) → pair (64, 495)
29. 66 divides 31680 (31680 ÷ 66 = 480) → pair (66, 480)
30. 72 divides 31680 (31680 ÷ 72 = 440) → pair (72, 440)
31. 80 divides 31680 (31680 ÷ 80 = 396) → pair (80, 396)
32. 88 divides 31680 (31680 ÷ 88 = 360) → pair (88, 360)
33. 90 divides 31680 (31680 ÷ 90 = 352) → pair (90, 352)
34. 96 divides 31680 (31680 ÷ 96 = 330) → pair (96, 330)
35. 99 divides 31680 (31680 ÷ 99 = 320) → pair (99, 320)
36. 110 divides 31680 (31680 ÷ 110 = 288) → pair (110, 288)
37. 120 divides 31680 (31680 ÷ 120 = 264) → pair (120, 264)
38. 132 divides 31680 (31680 ÷ 132 = 240) → pair (132, 240)
39. 144 divides 31680 (31680 ÷ 144 = 220) → pair (144, 220)
40. 160 divides 31680 (31680 ÷ 160 = 198) → pair (160, 198)
41. 165 divides 31680 (31680 ÷ 165 = 192) → pair (165, 192)
42. 176 divides 31680 (31680 ÷ 176 = 180) → pair (176, 180)
43. Collect all unique values: {1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 15, 16, 18, 20, 22, 24, 30, 32, 33, 36, 40, 44, 45, 48, 55, 60, 64, 66, 72, 80, 88, 90, 96, 99, 110, 120, 132, 144, 160, 165, 176, 180, 192, 198, 220, 240, 264, 288, 320, 330, 352, 360, 396, 440, 480, 495, 528, 576, 660, 704, 720, 792, 880, 960, 990, 1056, 1320, 1440, 1584, 1760, 1980, 2112, 2640, 2880, 3168, 3520, 3960, 5280, 6336, 7920, 10560, 15840, 31680} — total 84 divisors.
44. Sum: 1 + 2 + 3 + 4 + 5 + 6 + 8 + 9 + 10 + 11 + 12 + 15 + 16 + 18 + 20 + 22 + 24 + 30 + 32 + 33 + 36 + 40 + 44 + 45 + 48 + 55 + 60 + 64 + 66 + 72 + 80 + 88 + 90 + 96 + 99 + 110 + 120 + 132 + 144 + 160 + 165 + 176 + 180 + 192 + 198 + 220 + 240 + 264 + 288 + 320 + 330 + 352 + 360 + 396 + 440 + 480 + 495 + 528 + 576 + 660 + 704 + 720 + 792 + 880 + 960 + 990 + 1056 + 1320 + 1440 + 1584 + 1760 + 1980 + 2112 + 2640 + 2880 + 3168 + 3520 + 3960 + 5280 + 6336 + 7920 + 10560 + 15840 + 31680 = 118872.

Nearby Examples

Related Operations for 31680

• Multiples of a Number — "outward" complement of divisors
• 31680 Prime Factorization — decompose into prime building blocks
• Find GCF of 31680 and another number
• Find LCM of 31680 and another number
• Is 31680 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

Find all divisors of these numbers: