Divisors of 31920: All 80 Factors

Quick Answer

31920 has 80 divisors (factors): 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 19, 20, 21, 24, 28, 30, 35, 38, 40, 42, 48, 56, 57, 60, 70, 76, 80, 84, 95, 105, 112, 114, 120, 133, 140, 152, 168, 190, 210, 228, 240, 266, 280, 285, 304, 336, 380, 399, 420, 456, 532, 560, 570, 665, 760, 798, 840, 912, 1064, 1140, 1330, 1520, 1596, 1680, 1995, 2128, 2280, 2660, 3192, 3990, 4560, 5320, 6384, 7980, 10640, 15960, 31920.

Sum: 119040.

Divisors (Factors) Calculator

Divisors Multiples Prime Factoriz. GCF LCM

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80 divisors
1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 19, 20, 21, 24, 28, 30, 35, 38, 40, 42, 48, 56, 57, 60, 70, 76, 80, 84, 95, 105, 112, 114, 120, 133, 140, 152, 168, 190, 210, 228, 240, 266, 280, 285, 304, 336, 380, 399, 420, 456, 532, 560, 570, 665, 760, 798, 840, 912, 1064, 1140, 1330, 1520, 1596, 1680, 1995, 2128, 2280, 2660, 3192, 3990, 4560, 5320, 6384, 7980, 10640, 15960, 31920

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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 31920

The number 31920 has 80 divisors:

1,  2,  3,  4,  5,  6,  7,  8,  10,  12,  14,  15,  16,  19,  20,  21,  24,  28,  30,  35,  38,  40,  42,  48,  56,  57,  60,  70,  76,  80,  84,  95,  105,  112,  114,  120,  133,  140,  152,  168,  190,  210,  228,  240,  266,  280,  285,  304,  336,  380,  399,  420,  456,  532,  560,  570,  665,  760,  798,  840,  912,  1064,  1140,  1330,  1520,  1596,  1680,  1995,  2128,  2280,  2660,  3192,  3990,  4560,  5320,  6384,  7980,  10640,  15960,  31920

Divisor Pairs of 31920

Each pair multiplies to 31920:

Factor 1×Factor 2=Product
1×31920=31920
2×15960=31920
3×10640=31920
4×7980=31920
5×6384=31920
6×5320=31920
7×4560=31920
8×3990=31920
10×3192=31920
12×2660=31920
14×2280=31920
15×2128=31920
16×1995=31920
19×1680=31920
20×1596=31920
21×1520=31920
24×1330=31920
28×1140=31920
30×1064=31920
35×912=31920
38×840=31920
40×798=31920
42×760=31920
48×665=31920
56×570=31920
57×560=31920
60×532=31920
70×456=31920
76×420=31920
80×399=31920
84×380=31920
95×336=31920
105×304=31920
112×285=31920
114×280=31920
120×266=31920
133×240=31920
140×228=31920
152×210=31920
168×190=31920

Number of Divisors

The number 31920 has 80 divisors, written as τ(31920) = 80 in number theory.

Sum of Divisors

σ(31920) = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 10 + 12 + 14 + 15 + 16 + 19 + 20 + 21 + 24 + 28 + 30 + 35 + 38 + 40 + 42 + 48 + 56 + 57 + 60 + 70 + 76 + 80 + 84 + 95 + 105 + 112 + 114 + 120 + 133 + 140 + 152 + 168 + 190 + 210 + 228 + 240 + 266 + 280 + 285 + 304 + 336 + 380 + 399 + 420 + 456 + 532 + 560 + 570 + 665 + 760 + 798 + 840 + 912 + 1064 + 1140 + 1330 + 1520 + 1596 + 1680 + 1995 + 2128 + 2280 + 2660 + 3192 + 3990 + 4560 + 5320 + 6384 + 7980 + 10640 + 15960 + 31920 = 119040

Prime Factorization of 31920

See the full prime factorization calculator →

Properties of 31920

  • 31920 is composite.
  • 31920 is not a perfect square.
  • Number of divisors: 80.
  • Sum of divisors: 119040.

Common Divisors with Another Number?

Looking for the divisors that 31920 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 31920

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √31920 ≈ 178.66. If i divides 31920, then both i and 31920/i are divisors.

  1. 1 divides 31920 (31920 ÷ 1 = 31920) → pair (1, 31920)
  2. 2 divides 31920 (31920 ÷ 2 = 15960) → pair (2, 15960)
  3. 3 divides 31920 (31920 ÷ 3 = 10640) → pair (3, 10640)
  4. 4 divides 31920 (31920 ÷ 4 = 7980) → pair (4, 7980)
  5. 5 divides 31920 (31920 ÷ 5 = 6384) → pair (5, 6384)
  6. 6 divides 31920 (31920 ÷ 6 = 5320) → pair (6, 5320)
  7. 7 divides 31920 (31920 ÷ 7 = 4560) → pair (7, 4560)
  8. 8 divides 31920 (31920 ÷ 8 = 3990) → pair (8, 3990)
  9. 10 divides 31920 (31920 ÷ 10 = 3192) → pair (10, 3192)
  10. 12 divides 31920 (31920 ÷ 12 = 2660) → pair (12, 2660)
  11. 14 divides 31920 (31920 ÷ 14 = 2280) → pair (14, 2280)
  12. 15 divides 31920 (31920 ÷ 15 = 2128) → pair (15, 2128)
  13. 16 divides 31920 (31920 ÷ 16 = 1995) → pair (16, 1995)
  14. 19 divides 31920 (31920 ÷ 19 = 1680) → pair (19, 1680)
  15. 20 divides 31920 (31920 ÷ 20 = 1596) → pair (20, 1596)
  16. 21 divides 31920 (31920 ÷ 21 = 1520) → pair (21, 1520)
  17. 24 divides 31920 (31920 ÷ 24 = 1330) → pair (24, 1330)
  18. 28 divides 31920 (31920 ÷ 28 = 1140) → pair (28, 1140)
  19. 30 divides 31920 (31920 ÷ 30 = 1064) → pair (30, 1064)
  20. 35 divides 31920 (31920 ÷ 35 = 912) → pair (35, 912)
  21. 38 divides 31920 (31920 ÷ 38 = 840) → pair (38, 840)
  22. 40 divides 31920 (31920 ÷ 40 = 798) → pair (40, 798)
  23. 42 divides 31920 (31920 ÷ 42 = 760) → pair (42, 760)
  24. 48 divides 31920 (31920 ÷ 48 = 665) → pair (48, 665)
  25. 56 divides 31920 (31920 ÷ 56 = 570) → pair (56, 570)
  26. 57 divides 31920 (31920 ÷ 57 = 560) → pair (57, 560)
  27. 60 divides 31920 (31920 ÷ 60 = 532) → pair (60, 532)
  28. 70 divides 31920 (31920 ÷ 70 = 456) → pair (70, 456)
  29. 76 divides 31920 (31920 ÷ 76 = 420) → pair (76, 420)
  30. 80 divides 31920 (31920 ÷ 80 = 399) → pair (80, 399)
  31. 84 divides 31920 (31920 ÷ 84 = 380) → pair (84, 380)
  32. 95 divides 31920 (31920 ÷ 95 = 336) → pair (95, 336)
  33. 105 divides 31920 (31920 ÷ 105 = 304) → pair (105, 304)
  34. 112 divides 31920 (31920 ÷ 112 = 285) → pair (112, 285)
  35. 114 divides 31920 (31920 ÷ 114 = 280) → pair (114, 280)
  36. 120 divides 31920 (31920 ÷ 120 = 266) → pair (120, 266)
  37. 133 divides 31920 (31920 ÷ 133 = 240) → pair (133, 240)
  38. 140 divides 31920 (31920 ÷ 140 = 228) → pair (140, 228)
  39. 152 divides 31920 (31920 ÷ 152 = 210) → pair (152, 210)
  40. 168 divides 31920 (31920 ÷ 168 = 190) → pair (168, 190)
  41. Collect all unique values: {1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 19, 20, 21, 24, 28, 30, 35, 38, 40, 42, 48, 56, 57, 60, 70, 76, 80, 84, 95, 105, 112, 114, 120, 133, 140, 152, 168, 190, 210, 228, 240, 266, 280, 285, 304, 336, 380, 399, 420, 456, 532, 560, 570, 665, 760, 798, 840, 912, 1064, 1140, 1330, 1520, 1596, 1680, 1995, 2128, 2280, 2660, 3192, 3990, 4560, 5320, 6384, 7980, 10640, 15960, 31920} — total 80 divisors.
  42. Sum: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 10 + 12 + 14 + 15 + 16 + 19 + 20 + 21 + 24 + 28 + 30 + 35 + 38 + 40 + 42 + 48 + 56 + 57 + 60 + 70 + 76 + 80 + 84 + 95 + 105 + 112 + 114 + 120 + 133 + 140 + 152 + 168 + 190 + 210 + 228 + 240 + 266 + 280 + 285 + 304 + 336 + 380 + 399 + 420 + 456 + 532 + 560 + 570 + 665 + 760 + 798 + 840 + 912 + 1064 + 1140 + 1330 + 1520 + 1596 + 1680 + 1995 + 2128 + 2280 + 2660 + 3192 + 3990 + 4560 + 5320 + 6384 + 7980 + 10640 + 15960 + 31920 = 119040.

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Related Operations for 31920

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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

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