Divisors of 20160: All 84 Factors

Quick Answer

20160 has 84 divisors (factors): 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, 140, 144, 160, 168, 180, 192, 210, 224, 240, 252, 280, 288, 315, 320, 336, 360, 420, 448, 480, 504, 560, 576, 630, 672, 720, 840, 960, 1008, 1120, 1260, 1344, 1440, 1680, 2016, 2240, 2520, 2880, 3360, 4032, 5040, 6720, 10080, 20160.

Sum: 79248.

Divisors (Factors) Calculator

Divisors Multiples Prime Factoriz. GCF LCM

  Ex.: 12, 36, 100, 1024, 1728, etc.
84 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, 140, 144, 160, 168, 180, 192, 210, 224, 240, 252, 280, 288, 315, 320, 336, 360, 420, 448, 480, 504, 560, 576, 630, 672, 720, 840, 960, 1008, 1120, 1260, 1344, 1440, 1680, 2016, 2240, 2520, 2880, 3360, 4032, 5040, 6720, 10080, 20160

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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 20160

The number 20160 has 84 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,  140,  144,  160,  168,  180,  192,  210,  224,  240,  252,  280,  288,  315,  320,  336,  360,  420,  448,  480,  504,  560,  576,  630,  672,  720,  840,  960,  1008,  1120,  1260,  1344,  1440,  1680,  2016,  2240,  2520,  2880,  3360,  4032,  5040,  6720,  10080,  20160

Divisor Pairs of 20160

Each pair multiplies to 20160:

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

Number of Divisors

The number 20160 has 84 divisors, written as τ(20160) = 84 in number theory.

Sum of Divisors

σ(20160) = 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 + 140 + 144 + 160 + 168 + 180 + 192 + 210 + 224 + 240 + 252 + 280 + 288 + 315 + 320 + 336 + 360 + 420 + 448 + 480 + 504 + 560 + 576 + 630 + 672 + 720 + 840 + 960 + 1008 + 1120 + 1260 + 1344 + 1440 + 1680 + 2016 + 2240 + 2520 + 2880 + 3360 + 4032 + 5040 + 6720 + 10080 + 20160 = 79248

Prime Factorization of 20160

See the full prime factorization calculator →

Properties of 20160

  • 20160 is composite.
  • 20160 is not a perfect square.
  • Number of divisors: 84.
  • Sum of divisors: 79248.

Common Divisors with Another Number?

Looking for the divisors that 20160 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 20160

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √20160 ≈ 141.99. If i divides 20160, then both i and 20160/i are divisors.

  1. 1 divides 20160 (20160 ÷ 1 = 20160) → pair (1, 20160)
  2. 2 divides 20160 (20160 ÷ 2 = 10080) → pair (2, 10080)
  3. 3 divides 20160 (20160 ÷ 3 = 6720) → pair (3, 6720)
  4. 4 divides 20160 (20160 ÷ 4 = 5040) → pair (4, 5040)
  5. 5 divides 20160 (20160 ÷ 5 = 4032) → pair (5, 4032)
  6. 6 divides 20160 (20160 ÷ 6 = 3360) → pair (6, 3360)
  7. 7 divides 20160 (20160 ÷ 7 = 2880) → pair (7, 2880)
  8. 8 divides 20160 (20160 ÷ 8 = 2520) → pair (8, 2520)
  9. 9 divides 20160 (20160 ÷ 9 = 2240) → pair (9, 2240)
  10. 10 divides 20160 (20160 ÷ 10 = 2016) → pair (10, 2016)
  11. 12 divides 20160 (20160 ÷ 12 = 1680) → pair (12, 1680)
  12. 14 divides 20160 (20160 ÷ 14 = 1440) → pair (14, 1440)
  13. 15 divides 20160 (20160 ÷ 15 = 1344) → pair (15, 1344)
  14. 16 divides 20160 (20160 ÷ 16 = 1260) → pair (16, 1260)
  15. 18 divides 20160 (20160 ÷ 18 = 1120) → pair (18, 1120)
  16. 20 divides 20160 (20160 ÷ 20 = 1008) → pair (20, 1008)
  17. 21 divides 20160 (20160 ÷ 21 = 960) → pair (21, 960)
  18. 24 divides 20160 (20160 ÷ 24 = 840) → pair (24, 840)
  19. 28 divides 20160 (20160 ÷ 28 = 720) → pair (28, 720)
  20. 30 divides 20160 (20160 ÷ 30 = 672) → pair (30, 672)
  21. 32 divides 20160 (20160 ÷ 32 = 630) → pair (32, 630)
  22. 35 divides 20160 (20160 ÷ 35 = 576) → pair (35, 576)
  23. 36 divides 20160 (20160 ÷ 36 = 560) → pair (36, 560)
  24. 40 divides 20160 (20160 ÷ 40 = 504) → pair (40, 504)
  25. 42 divides 20160 (20160 ÷ 42 = 480) → pair (42, 480)
  26. 45 divides 20160 (20160 ÷ 45 = 448) → pair (45, 448)
  27. 48 divides 20160 (20160 ÷ 48 = 420) → pair (48, 420)
  28. 56 divides 20160 (20160 ÷ 56 = 360) → pair (56, 360)
  29. 60 divides 20160 (20160 ÷ 60 = 336) → pair (60, 336)
  30. 63 divides 20160 (20160 ÷ 63 = 320) → pair (63, 320)
  31. 64 divides 20160 (20160 ÷ 64 = 315) → pair (64, 315)
  32. 70 divides 20160 (20160 ÷ 70 = 288) → pair (70, 288)
  33. 72 divides 20160 (20160 ÷ 72 = 280) → pair (72, 280)
  34. 80 divides 20160 (20160 ÷ 80 = 252) → pair (80, 252)
  35. 84 divides 20160 (20160 ÷ 84 = 240) → pair (84, 240)
  36. 90 divides 20160 (20160 ÷ 90 = 224) → pair (90, 224)
  37. 96 divides 20160 (20160 ÷ 96 = 210) → pair (96, 210)
  38. 105 divides 20160 (20160 ÷ 105 = 192) → pair (105, 192)
  39. 112 divides 20160 (20160 ÷ 112 = 180) → pair (112, 180)
  40. 120 divides 20160 (20160 ÷ 120 = 168) → pair (120, 168)
  41. 126 divides 20160 (20160 ÷ 126 = 160) → pair (126, 160)
  42. 140 divides 20160 (20160 ÷ 140 = 144) → pair (140, 144)
  43. 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, 140, 144, 160, 168, 180, 192, 210, 224, 240, 252, 280, 288, 315, 320, 336, 360, 420, 448, 480, 504, 560, 576, 630, 672, 720, 840, 960, 1008, 1120, 1260, 1344, 1440, 1680, 2016, 2240, 2520, 2880, 3360, 4032, 5040, 6720, 10080, 20160} — total 84 divisors.
  44. 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 + 140 + 144 + 160 + 168 + 180 + 192 + 210 + 224 + 240 + 252 + 280 + 288 + 315 + 320 + 336 + 360 + 420 + 448 + 480 + 504 + 560 + 576 + 630 + 672 + 720 + 840 + 960 + 1008 + 1120 + 1260 + 1344 + 1440 + 1680 + 2016 + 2240 + 2520 + 2880 + 3360 + 4032 + 5040 + 6720 + 10080 + 20160 = 79248.

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Related Operations for 20160

See also our tables of divisors:

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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