Divisors of 36000: All 72 Factors

Quick Answer

36000 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, 72, 75, 80, 90, 96, 100, 120, 125, 144, 150, 160, 180, 200, 225, 240, 250, 288, 300, 360, 375, 400, 450, 480, 500, 600, 720, 750, 800, 900, 1000, 1125, 1200, 1440, 1500, 1800, 2000, 2250, 2400, 3000, 3600, 4000, 4500, 6000, 7200, 9000, 12000, 18000, 36000.

Sum: 127764.

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, 72, 75, 80, 90, 96, 100, 120, 125, 144, 150, 160, 180, 200, 225, 240, 250, 288, 300, 360, 375, 400, 450, 480, 500, 600, 720, 750, 800, 900, 1000, 1125, 1200, 1440, 1500, 1800, 2000, 2250, 2400, 3000, 3600, 4000, 4500, 6000, 7200, 9000, 12000, 18000, 36000

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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 36000

The number 36000 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,  72,  75,  80,  90,  96,  100,  120,  125,  144,  150,  160,  180,  200,  225,  240,  250,  288,  300,  360,  375,  400,  450,  480,  500,  600,  720,  750,  800,  900,  1000,  1125,  1200,  1440,  1500,  1800,  2000,  2250,  2400,  3000,  3600,  4000,  4500,  6000,  7200,  9000,  12000,  18000,  36000

Divisor Pairs of 36000

Each pair multiplies to 36000:

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

Number of Divisors

The number 36000 has 72 divisors, written as τ(36000) = 72 in number theory.

Sum of Divisors

σ(36000) = 1 + 2 + 3 + 4 + 5 + 6 + 8 + 9 + 10 + 12 + 15 + 16 + 18 + 20 + 24 + 25 + 30 + 32 + 36 + 40 + 45 + 48 + 50 + 60 + 72 + 75 + 80 + 90 + 96 + 100 + 120 + 125 + 144 + 150 + 160 + 180 + 200 + 225 + 240 + 250 + 288 + 300 + 360 + 375 + 400 + 450 + 480 + 500 + 600 + 720 + 750 + 800 + 900 + 1000 + 1125 + 1200 + 1440 + 1500 + 1800 + 2000 + 2250 + 2400 + 3000 + 3600 + 4000 + 4500 + 6000 + 7200 + 9000 + 12000 + 18000 + 36000 = 127764

Prime Factorization of 36000

See the full prime factorization calculator →

Properties of 36000

  • 36000 is composite.
  • 36000 is not a perfect square.
  • Number of divisors: 72.
  • Sum of divisors: 127764.

Common Divisors with Another Number?

Looking for the divisors that 36000 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 36000

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √36000 ≈ 189.74. If i divides 36000, then both i and 36000/i are divisors.

  1. 1 divides 36000 (36000 ÷ 1 = 36000) → pair (1, 36000)
  2. 2 divides 36000 (36000 ÷ 2 = 18000) → pair (2, 18000)
  3. 3 divides 36000 (36000 ÷ 3 = 12000) → pair (3, 12000)
  4. 4 divides 36000 (36000 ÷ 4 = 9000) → pair (4, 9000)
  5. 5 divides 36000 (36000 ÷ 5 = 7200) → pair (5, 7200)
  6. 6 divides 36000 (36000 ÷ 6 = 6000) → pair (6, 6000)
  7. 8 divides 36000 (36000 ÷ 8 = 4500) → pair (8, 4500)
  8. 9 divides 36000 (36000 ÷ 9 = 4000) → pair (9, 4000)
  9. 10 divides 36000 (36000 ÷ 10 = 3600) → pair (10, 3600)
  10. 12 divides 36000 (36000 ÷ 12 = 3000) → pair (12, 3000)
  11. 15 divides 36000 (36000 ÷ 15 = 2400) → pair (15, 2400)
  12. 16 divides 36000 (36000 ÷ 16 = 2250) → pair (16, 2250)
  13. 18 divides 36000 (36000 ÷ 18 = 2000) → pair (18, 2000)
  14. 20 divides 36000 (36000 ÷ 20 = 1800) → pair (20, 1800)
  15. 24 divides 36000 (36000 ÷ 24 = 1500) → pair (24, 1500)
  16. 25 divides 36000 (36000 ÷ 25 = 1440) → pair (25, 1440)
  17. 30 divides 36000 (36000 ÷ 30 = 1200) → pair (30, 1200)
  18. 32 divides 36000 (36000 ÷ 32 = 1125) → pair (32, 1125)
  19. 36 divides 36000 (36000 ÷ 36 = 1000) → pair (36, 1000)
  20. 40 divides 36000 (36000 ÷ 40 = 900) → pair (40, 900)
  21. 45 divides 36000 (36000 ÷ 45 = 800) → pair (45, 800)
  22. 48 divides 36000 (36000 ÷ 48 = 750) → pair (48, 750)
  23. 50 divides 36000 (36000 ÷ 50 = 720) → pair (50, 720)
  24. 60 divides 36000 (36000 ÷ 60 = 600) → pair (60, 600)
  25. 72 divides 36000 (36000 ÷ 72 = 500) → pair (72, 500)
  26. 75 divides 36000 (36000 ÷ 75 = 480) → pair (75, 480)
  27. 80 divides 36000 (36000 ÷ 80 = 450) → pair (80, 450)
  28. 90 divides 36000 (36000 ÷ 90 = 400) → pair (90, 400)
  29. 96 divides 36000 (36000 ÷ 96 = 375) → pair (96, 375)
  30. 100 divides 36000 (36000 ÷ 100 = 360) → pair (100, 360)
  31. 120 divides 36000 (36000 ÷ 120 = 300) → pair (120, 300)
  32. 125 divides 36000 (36000 ÷ 125 = 288) → pair (125, 288)
  33. 144 divides 36000 (36000 ÷ 144 = 250) → pair (144, 250)
  34. 150 divides 36000 (36000 ÷ 150 = 240) → pair (150, 240)
  35. 160 divides 36000 (36000 ÷ 160 = 225) → pair (160, 225)
  36. 180 divides 36000 (36000 ÷ 180 = 200) → pair (180, 200)
  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, 72, 75, 80, 90, 96, 100, 120, 125, 144, 150, 160, 180, 200, 225, 240, 250, 288, 300, 360, 375, 400, 450, 480, 500, 600, 720, 750, 800, 900, 1000, 1125, 1200, 1440, 1500, 1800, 2000, 2250, 2400, 3000, 3600, 4000, 4500, 6000, 7200, 9000, 12000, 18000, 36000} — 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 + 72 + 75 + 80 + 90 + 96 + 100 + 120 + 125 + 144 + 150 + 160 + 180 + 200 + 225 + 240 + 250 + 288 + 300 + 360 + 375 + 400 + 450 + 480 + 500 + 600 + 720 + 750 + 800 + 900 + 1000 + 1125 + 1200 + 1440 + 1500 + 1800 + 2000 + 2250 + 2400 + 3000 + 3600 + 4000 + 4500 + 6000 + 7200 + 9000 + 12000 + 18000 + 36000 = 127764.

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Related Operations for 36000

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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