Divisors of 21600: All 72 Factors

Quick Answer

21600 has 72 divisors (factors): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 32, 36, 40, 45, 48, 50, 54, 60, 72, 75, 80, 90, 96, 100, 108, 120, 135, 144, 150, 160, 180, 200, 216, 225, 240, 270, 288, 300, 360, 400, 432, 450, 480, 540, 600, 675, 720, 800, 864, 900, 1080, 1200, 1350, 1440, 1800, 2160, 2400, 2700, 3600, 4320, 5400, 7200, 10800, 21600.

Sum: 78120.

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, 27, 30, 32, 36, 40, 45, 48, 50, 54, 60, 72, 75, 80, 90, 96, 100, 108, 120, 135, 144, 150, 160, 180, 200, 216, 225, 240, 270, 288, 300, 360, 400, 432, 450, 480, 540, 600, 675, 720, 800, 864, 900, 1080, 1200, 1350, 1440, 1800, 2160, 2400, 2700, 3600, 4320, 5400, 7200, 10800, 21600

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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 21600

The number 21600 has 72 divisors:

1,  2,  3,  4,  5,  6,  8,  9,  10,  12,  15,  16,  18,  20,  24,  25,  27,  30,  32,  36,  40,  45,  48,  50,  54,  60,  72,  75,  80,  90,  96,  100,  108,  120,  135,  144,  150,  160,  180,  200,  216,  225,  240,  270,  288,  300,  360,  400,  432,  450,  480,  540,  600,  675,  720,  800,  864,  900,  1080,  1200,  1350,  1440,  1800,  2160,  2400,  2700,  3600,  4320,  5400,  7200,  10800,  21600

Divisor Pairs of 21600

Each pair multiplies to 21600:

Factor 1×Factor 2=Product
1×21600=21600
2×10800=21600
3×7200=21600
4×5400=21600
5×4320=21600
6×3600=21600
8×2700=21600
9×2400=21600
10×2160=21600
12×1800=21600
15×1440=21600
16×1350=21600
18×1200=21600
20×1080=21600
24×900=21600
25×864=21600
27×800=21600
30×720=21600
32×675=21600
36×600=21600
40×540=21600
45×480=21600
48×450=21600
50×432=21600
54×400=21600
60×360=21600
72×300=21600
75×288=21600
80×270=21600
90×240=21600
96×225=21600
100×216=21600
108×200=21600
120×180=21600
135×160=21600
144×150=21600

Number of Divisors

The number 21600 has 72 divisors, written as τ(21600) = 72 in number theory.

Sum of Divisors

σ(21600) = 1 + 2 + 3 + 4 + 5 + 6 + 8 + 9 + 10 + 12 + 15 + 16 + 18 + 20 + 24 + 25 + 27 + 30 + 32 + 36 + 40 + 45 + 48 + 50 + 54 + 60 + 72 + 75 + 80 + 90 + 96 + 100 + 108 + 120 + 135 + 144 + 150 + 160 + 180 + 200 + 216 + 225 + 240 + 270 + 288 + 300 + 360 + 400 + 432 + 450 + 480 + 540 + 600 + 675 + 720 + 800 + 864 + 900 + 1080 + 1200 + 1350 + 1440 + 1800 + 2160 + 2400 + 2700 + 3600 + 4320 + 5400 + 7200 + 10800 + 21600 = 78120

Prime Factorization of 21600

See the full prime factorization calculator →

Properties of 21600

  • 21600 is composite.
  • 21600 is not a perfect square.
  • Number of divisors: 72.
  • Sum of divisors: 78120.

Common Divisors with Another Number?

Looking for the divisors that 21600 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 21600

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √21600 ≈ 146.97. If i divides 21600, then both i and 21600/i are divisors.

  1. 1 divides 21600 (21600 ÷ 1 = 21600) → pair (1, 21600)
  2. 2 divides 21600 (21600 ÷ 2 = 10800) → pair (2, 10800)
  3. 3 divides 21600 (21600 ÷ 3 = 7200) → pair (3, 7200)
  4. 4 divides 21600 (21600 ÷ 4 = 5400) → pair (4, 5400)
  5. 5 divides 21600 (21600 ÷ 5 = 4320) → pair (5, 4320)
  6. 6 divides 21600 (21600 ÷ 6 = 3600) → pair (6, 3600)
  7. 8 divides 21600 (21600 ÷ 8 = 2700) → pair (8, 2700)
  8. 9 divides 21600 (21600 ÷ 9 = 2400) → pair (9, 2400)
  9. 10 divides 21600 (21600 ÷ 10 = 2160) → pair (10, 2160)
  10. 12 divides 21600 (21600 ÷ 12 = 1800) → pair (12, 1800)
  11. 15 divides 21600 (21600 ÷ 15 = 1440) → pair (15, 1440)
  12. 16 divides 21600 (21600 ÷ 16 = 1350) → pair (16, 1350)
  13. 18 divides 21600 (21600 ÷ 18 = 1200) → pair (18, 1200)
  14. 20 divides 21600 (21600 ÷ 20 = 1080) → pair (20, 1080)
  15. 24 divides 21600 (21600 ÷ 24 = 900) → pair (24, 900)
  16. 25 divides 21600 (21600 ÷ 25 = 864) → pair (25, 864)
  17. 27 divides 21600 (21600 ÷ 27 = 800) → pair (27, 800)
  18. 30 divides 21600 (21600 ÷ 30 = 720) → pair (30, 720)
  19. 32 divides 21600 (21600 ÷ 32 = 675) → pair (32, 675)
  20. 36 divides 21600 (21600 ÷ 36 = 600) → pair (36, 600)
  21. 40 divides 21600 (21600 ÷ 40 = 540) → pair (40, 540)
  22. 45 divides 21600 (21600 ÷ 45 = 480) → pair (45, 480)
  23. 48 divides 21600 (21600 ÷ 48 = 450) → pair (48, 450)
  24. 50 divides 21600 (21600 ÷ 50 = 432) → pair (50, 432)
  25. 54 divides 21600 (21600 ÷ 54 = 400) → pair (54, 400)
  26. 60 divides 21600 (21600 ÷ 60 = 360) → pair (60, 360)
  27. 72 divides 21600 (21600 ÷ 72 = 300) → pair (72, 300)
  28. 75 divides 21600 (21600 ÷ 75 = 288) → pair (75, 288)
  29. 80 divides 21600 (21600 ÷ 80 = 270) → pair (80, 270)
  30. 90 divides 21600 (21600 ÷ 90 = 240) → pair (90, 240)
  31. 96 divides 21600 (21600 ÷ 96 = 225) → pair (96, 225)
  32. 100 divides 21600 (21600 ÷ 100 = 216) → pair (100, 216)
  33. 108 divides 21600 (21600 ÷ 108 = 200) → pair (108, 200)
  34. 120 divides 21600 (21600 ÷ 120 = 180) → pair (120, 180)
  35. 135 divides 21600 (21600 ÷ 135 = 160) → pair (135, 160)
  36. 144 divides 21600 (21600 ÷ 144 = 150) → pair (144, 150)
  37. Collect all unique values: {1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 32, 36, 40, 45, 48, 50, 54, 60, 72, 75, 80, 90, 96, 100, 108, 120, 135, 144, 150, 160, 180, 200, 216, 225, 240, 270, 288, 300, 360, 400, 432, 450, 480, 540, 600, 675, 720, 800, 864, 900, 1080, 1200, 1350, 1440, 1800, 2160, 2400, 2700, 3600, 4320, 5400, 7200, 10800, 21600} — total 72 divisors.
  38. Sum: 1 + 2 + 3 + 4 + 5 + 6 + 8 + 9 + 10 + 12 + 15 + 16 + 18 + 20 + 24 + 25 + 27 + 30 + 32 + 36 + 40 + 45 + 48 + 50 + 54 + 60 + 72 + 75 + 80 + 90 + 96 + 100 + 108 + 120 + 135 + 144 + 150 + 160 + 180 + 200 + 216 + 225 + 240 + 270 + 288 + 300 + 360 + 400 + 432 + 450 + 480 + 540 + 600 + 675 + 720 + 800 + 864 + 900 + 1080 + 1200 + 1350 + 1440 + 1800 + 2160 + 2400 + 2700 + 3600 + 4320 + 5400 + 7200 + 10800 + 21600 = 78120.

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Related Operations for 21600

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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