Divisors of 28800: All 72 Factors

Quick Answer

28800 has 72 divisors (factors): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 32, 36, 40, 45, 48, 50, 60, 64, 72, 75, 80, 90, 96, 100, 120, 128, 144, 150, 160, 180, 192, 200, 225, 240, 288, 300, 320, 360, 384, 400, 450, 480, 576, 600, 640, 720, 800, 900, 960, 1152, 1200, 1440, 1600, 1800, 1920, 2400, 2880, 3200, 3600, 4800, 5760, 7200, 9600, 14400, 28800.

Sum: 102765.

Divisors (Factors) Calculator

Divisors Multiples Prime Factoriz. GCF LCM

  Ex.: 12, 36, 100, 1024, 1728, etc.
72 divisors
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 32, 36, 40, 45, 48, 50, 60, 64, 72, 75, 80, 90, 96, 100, 120, 128, 144, 150, 160, 180, 192, 200, 225, 240, 288, 300, 320, 360, 384, 400, 450, 480, 576, 600, 640, 720, 800, 900, 960, 1152, 1200, 1440, 1600, 1800, 1920, 2400, 2880, 3200, 3600, 4800, 5760, 7200, 9600, 14400, 28800

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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 28800

The number 28800 has 72 divisors:

1,  2,  3,  4,  5,  6,  8,  9,  10,  12,  15,  16,  18,  20,  24,  25,  30,  32,  36,  40,  45,  48,  50,  60,  64,  72,  75,  80,  90,  96,  100,  120,  128,  144,  150,  160,  180,  192,  200,  225,  240,  288,  300,  320,  360,  384,  400,  450,  480,  576,  600,  640,  720,  800,  900,  960,  1152,  1200,  1440,  1600,  1800,  1920,  2400,  2880,  3200,  3600,  4800,  5760,  7200,  9600,  14400,  28800

Divisor Pairs of 28800

Each pair multiplies to 28800:

Factor 1×Factor 2=Product
1×28800=28800
2×14400=28800
3×9600=28800
4×7200=28800
5×5760=28800
6×4800=28800
8×3600=28800
9×3200=28800
10×2880=28800
12×2400=28800
15×1920=28800
16×1800=28800
18×1600=28800
20×1440=28800
24×1200=28800
25×1152=28800
30×960=28800
32×900=28800
36×800=28800
40×720=28800
45×640=28800
48×600=28800
50×576=28800
60×480=28800
64×450=28800
72×400=28800
75×384=28800
80×360=28800
90×320=28800
96×300=28800
100×288=28800
120×240=28800
128×225=28800
144×200=28800
150×192=28800
160×180=28800

Number of Divisors

The number 28800 has 72 divisors, written as τ(28800) = 72 in number theory.

Sum of Divisors

σ(28800) = 1 + 2 + 3 + 4 + 5 + 6 + 8 + 9 + 10 + 12 + 15 + 16 + 18 + 20 + 24 + 25 + 30 + 32 + 36 + 40 + 45 + 48 + 50 + 60 + 64 + 72 + 75 + 80 + 90 + 96 + 100 + 120 + 128 + 144 + 150 + 160 + 180 + 192 + 200 + 225 + 240 + 288 + 300 + 320 + 360 + 384 + 400 + 450 + 480 + 576 + 600 + 640 + 720 + 800 + 900 + 960 + 1152 + 1200 + 1440 + 1600 + 1800 + 1920 + 2400 + 2880 + 3200 + 3600 + 4800 + 5760 + 7200 + 9600 + 14400 + 28800 = 102765

Prime Factorization of 28800

See the full prime factorization calculator →

Properties of 28800

  • 28800 is composite.
  • 28800 is not a perfect square.
  • Number of divisors: 72.
  • Sum of divisors: 102765.

Common Divisors with Another Number?

Looking for the divisors that 28800 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 28800

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √28800 ≈ 169.71. If i divides 28800, then both i and 28800/i are divisors.

  1. 1 divides 28800 (28800 ÷ 1 = 28800) → pair (1, 28800)
  2. 2 divides 28800 (28800 ÷ 2 = 14400) → pair (2, 14400)
  3. 3 divides 28800 (28800 ÷ 3 = 9600) → pair (3, 9600)
  4. 4 divides 28800 (28800 ÷ 4 = 7200) → pair (4, 7200)
  5. 5 divides 28800 (28800 ÷ 5 = 5760) → pair (5, 5760)
  6. 6 divides 28800 (28800 ÷ 6 = 4800) → pair (6, 4800)
  7. 8 divides 28800 (28800 ÷ 8 = 3600) → pair (8, 3600)
  8. 9 divides 28800 (28800 ÷ 9 = 3200) → pair (9, 3200)
  9. 10 divides 28800 (28800 ÷ 10 = 2880) → pair (10, 2880)
  10. 12 divides 28800 (28800 ÷ 12 = 2400) → pair (12, 2400)
  11. 15 divides 28800 (28800 ÷ 15 = 1920) → pair (15, 1920)
  12. 16 divides 28800 (28800 ÷ 16 = 1800) → pair (16, 1800)
  13. 18 divides 28800 (28800 ÷ 18 = 1600) → pair (18, 1600)
  14. 20 divides 28800 (28800 ÷ 20 = 1440) → pair (20, 1440)
  15. 24 divides 28800 (28800 ÷ 24 = 1200) → pair (24, 1200)
  16. 25 divides 28800 (28800 ÷ 25 = 1152) → pair (25, 1152)
  17. 30 divides 28800 (28800 ÷ 30 = 960) → pair (30, 960)
  18. 32 divides 28800 (28800 ÷ 32 = 900) → pair (32, 900)
  19. 36 divides 28800 (28800 ÷ 36 = 800) → pair (36, 800)
  20. 40 divides 28800 (28800 ÷ 40 = 720) → pair (40, 720)
  21. 45 divides 28800 (28800 ÷ 45 = 640) → pair (45, 640)
  22. 48 divides 28800 (28800 ÷ 48 = 600) → pair (48, 600)
  23. 50 divides 28800 (28800 ÷ 50 = 576) → pair (50, 576)
  24. 60 divides 28800 (28800 ÷ 60 = 480) → pair (60, 480)
  25. 64 divides 28800 (28800 ÷ 64 = 450) → pair (64, 450)
  26. 72 divides 28800 (28800 ÷ 72 = 400) → pair (72, 400)
  27. 75 divides 28800 (28800 ÷ 75 = 384) → pair (75, 384)
  28. 80 divides 28800 (28800 ÷ 80 = 360) → pair (80, 360)
  29. 90 divides 28800 (28800 ÷ 90 = 320) → pair (90, 320)
  30. 96 divides 28800 (28800 ÷ 96 = 300) → pair (96, 300)
  31. 100 divides 28800 (28800 ÷ 100 = 288) → pair (100, 288)
  32. 120 divides 28800 (28800 ÷ 120 = 240) → pair (120, 240)
  33. 128 divides 28800 (28800 ÷ 128 = 225) → pair (128, 225)
  34. 144 divides 28800 (28800 ÷ 144 = 200) → pair (144, 200)
  35. 150 divides 28800 (28800 ÷ 150 = 192) → pair (150, 192)
  36. 160 divides 28800 (28800 ÷ 160 = 180) → pair (160, 180)
  37. Collect all unique values: {1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 32, 36, 40, 45, 48, 50, 60, 64, 72, 75, 80, 90, 96, 100, 120, 128, 144, 150, 160, 180, 192, 200, 225, 240, 288, 300, 320, 360, 384, 400, 450, 480, 576, 600, 640, 720, 800, 900, 960, 1152, 1200, 1440, 1600, 1800, 1920, 2400, 2880, 3200, 3600, 4800, 5760, 7200, 9600, 14400, 28800} — total 72 divisors.
  38. Sum: 1 + 2 + 3 + 4 + 5 + 6 + 8 + 9 + 10 + 12 + 15 + 16 + 18 + 20 + 24 + 25 + 30 + 32 + 36 + 40 + 45 + 48 + 50 + 60 + 64 + 72 + 75 + 80 + 90 + 96 + 100 + 120 + 128 + 144 + 150 + 160 + 180 + 192 + 200 + 225 + 240 + 288 + 300 + 320 + 360 + 384 + 400 + 450 + 480 + 576 + 600 + 640 + 720 + 800 + 900 + 960 + 1152 + 1200 + 1440 + 1600 + 1800 + 1920 + 2400 + 2880 + 3200 + 3600 + 4800 + 5760 + 7200 + 9600 + 14400 + 28800 = 102765.

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Related Operations for 28800

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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