Divisors of 72000: All 84 Factors

Quick Answer

72000 has 84 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, 125, 144, 150, 160, 180, 192, 200, 225, 240, 250, 288, 300, 320, 360, 375, 400, 450, 480, 500, 576, 600, 720, 750, 800, 900, 960, 1000, 1125, 1200, 1440, 1500, 1600, 1800, 2000, 2250, 2400, 2880, 3000, 3600, 4000, 4500, 4800, 6000, 7200, 8000, 9000, 12000, 14400, 18000, 24000, 36000, 72000.

Sum: 257556.

Divisors (Factors) Calculator

Divisors Multiples Prime Factoriz. GCF LCM

  Ex.: 12, 36, 100, 1024, 1728, etc.
84 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, 125, 144, 150, 160, 180, 192, 200, 225, 240, 250, 288, 300, 320, 360, 375, 400, 450, 480, 500, 576, 600, 720, 750, 800, 900, 960, 1000, 1125, 1200, 1440, 1500, 1600, 1800, 2000, 2250, 2400, 2880, 3000, 3600, 4000, 4500, 4800, 6000, 7200, 8000, 9000, 12000, 14400, 18000, 24000, 36000, 72000

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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 72000

The number 72000 has 84 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,  125,  144,  150,  160,  180,  192,  200,  225,  240,  250,  288,  300,  320,  360,  375,  400,  450,  480,  500,  576,  600,  720,  750,  800,  900,  960,  1000,  1125,  1200,  1440,  1500,  1600,  1800,  2000,  2250,  2400,  2880,  3000,  3600,  4000,  4500,  4800,  6000,  7200,  8000,  9000,  12000,  14400,  18000,  24000,  36000,  72000

Divisor Pairs of 72000

Each pair multiplies to 72000:

Factor 1×Factor 2=Product
1×72000=72000
2×36000=72000
3×24000=72000
4×18000=72000
5×14400=72000
6×12000=72000
8×9000=72000
9×8000=72000
10×7200=72000
12×6000=72000
15×4800=72000
16×4500=72000
18×4000=72000
20×3600=72000
24×3000=72000
25×2880=72000
30×2400=72000
32×2250=72000
36×2000=72000
40×1800=72000
45×1600=72000
48×1500=72000
50×1440=72000
60×1200=72000
64×1125=72000
72×1000=72000
75×960=72000
80×900=72000
90×800=72000
96×750=72000
100×720=72000
120×600=72000
125×576=72000
144×500=72000
150×480=72000
160×450=72000
180×400=72000
192×375=72000
200×360=72000
225×320=72000
240×300=72000
250×288=72000

Number of Divisors

The number 72000 has 84 divisors, written as τ(72000) = 84 in number theory.

Sum of Divisors

σ(72000) = 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 + 125 + 144 + 150 + 160 + 180 + 192 + 200 + 225 + 240 + 250 + 288 + 300 + 320 + 360 + 375 + 400 + 450 + 480 + 500 + 576 + 600 + 720 + 750 + 800 + 900 + 960 + 1000 + 1125 + 1200 + 1440 + 1500 + 1600 + 1800 + 2000 + 2250 + 2400 + 2880 + 3000 + 3600 + 4000 + 4500 + 4800 + 6000 + 7200 + 8000 + 9000 + 12000 + 14400 + 18000 + 24000 + 36000 + 72000 = 257556

Prime Factorization of 72000

See the full prime factorization calculator →

Properties of 72000

  • 72000 is composite.
  • 72000 is not a perfect square.
  • Number of divisors: 84.
  • Sum of divisors: 257556.

Common Divisors with Another Number?

Looking for the divisors that 72000 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 72000

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √72000 ≈ 268.33. If i divides 72000, then both i and 72000/i are divisors.

  1. 1 divides 72000 (72000 ÷ 1 = 72000) → pair (1, 72000)
  2. 2 divides 72000 (72000 ÷ 2 = 36000) → pair (2, 36000)
  3. 3 divides 72000 (72000 ÷ 3 = 24000) → pair (3, 24000)
  4. 4 divides 72000 (72000 ÷ 4 = 18000) → pair (4, 18000)
  5. 5 divides 72000 (72000 ÷ 5 = 14400) → pair (5, 14400)
  6. 6 divides 72000 (72000 ÷ 6 = 12000) → pair (6, 12000)
  7. 8 divides 72000 (72000 ÷ 8 = 9000) → pair (8, 9000)
  8. 9 divides 72000 (72000 ÷ 9 = 8000) → pair (9, 8000)
  9. 10 divides 72000 (72000 ÷ 10 = 7200) → pair (10, 7200)
  10. 12 divides 72000 (72000 ÷ 12 = 6000) → pair (12, 6000)
  11. 15 divides 72000 (72000 ÷ 15 = 4800) → pair (15, 4800)
  12. 16 divides 72000 (72000 ÷ 16 = 4500) → pair (16, 4500)
  13. 18 divides 72000 (72000 ÷ 18 = 4000) → pair (18, 4000)
  14. 20 divides 72000 (72000 ÷ 20 = 3600) → pair (20, 3600)
  15. 24 divides 72000 (72000 ÷ 24 = 3000) → pair (24, 3000)
  16. 25 divides 72000 (72000 ÷ 25 = 2880) → pair (25, 2880)
  17. 30 divides 72000 (72000 ÷ 30 = 2400) → pair (30, 2400)
  18. 32 divides 72000 (72000 ÷ 32 = 2250) → pair (32, 2250)
  19. 36 divides 72000 (72000 ÷ 36 = 2000) → pair (36, 2000)
  20. 40 divides 72000 (72000 ÷ 40 = 1800) → pair (40, 1800)
  21. 45 divides 72000 (72000 ÷ 45 = 1600) → pair (45, 1600)
  22. 48 divides 72000 (72000 ÷ 48 = 1500) → pair (48, 1500)
  23. 50 divides 72000 (72000 ÷ 50 = 1440) → pair (50, 1440)
  24. 60 divides 72000 (72000 ÷ 60 = 1200) → pair (60, 1200)
  25. 64 divides 72000 (72000 ÷ 64 = 1125) → pair (64, 1125)
  26. 72 divides 72000 (72000 ÷ 72 = 1000) → pair (72, 1000)
  27. 75 divides 72000 (72000 ÷ 75 = 960) → pair (75, 960)
  28. 80 divides 72000 (72000 ÷ 80 = 900) → pair (80, 900)
  29. 90 divides 72000 (72000 ÷ 90 = 800) → pair (90, 800)
  30. 96 divides 72000 (72000 ÷ 96 = 750) → pair (96, 750)
  31. 100 divides 72000 (72000 ÷ 100 = 720) → pair (100, 720)
  32. 120 divides 72000 (72000 ÷ 120 = 600) → pair (120, 600)
  33. 125 divides 72000 (72000 ÷ 125 = 576) → pair (125, 576)
  34. 144 divides 72000 (72000 ÷ 144 = 500) → pair (144, 500)
  35. 150 divides 72000 (72000 ÷ 150 = 480) → pair (150, 480)
  36. 160 divides 72000 (72000 ÷ 160 = 450) → pair (160, 450)
  37. 180 divides 72000 (72000 ÷ 180 = 400) → pair (180, 400)
  38. 192 divides 72000 (72000 ÷ 192 = 375) → pair (192, 375)
  39. 200 divides 72000 (72000 ÷ 200 = 360) → pair (200, 360)
  40. 225 divides 72000 (72000 ÷ 225 = 320) → pair (225, 320)
  41. 240 divides 72000 (72000 ÷ 240 = 300) → pair (240, 300)
  42. 250 divides 72000 (72000 ÷ 250 = 288) → pair (250, 288)
  43. 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, 125, 144, 150, 160, 180, 192, 200, 225, 240, 250, 288, 300, 320, 360, 375, 400, 450, 480, 500, 576, 600, 720, 750, 800, 900, 960, 1000, 1125, 1200, 1440, 1500, 1600, 1800, 2000, 2250, 2400, 2880, 3000, 3600, 4000, 4500, 4800, 6000, 7200, 8000, 9000, 12000, 14400, 18000, 24000, 36000, 72000} — total 84 divisors.
  44. 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 + 125 + 144 + 150 + 160 + 180 + 192 + 200 + 225 + 240 + 250 + 288 + 300 + 320 + 360 + 375 + 400 + 450 + 480 + 500 + 576 + 600 + 720 + 750 + 800 + 900 + 960 + 1000 + 1125 + 1200 + 1440 + 1500 + 1600 + 1800 + 2000 + 2250 + 2400 + 2880 + 3000 + 3600 + 4000 + 4500 + 4800 + 6000 + 7200 + 8000 + 9000 + 12000 + 14400 + 18000 + 24000 + 36000 + 72000 = 257556.

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Related Operations for 72000

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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