Divisors of 32400: All 75 Factors

Quick Answer

32400 has 75 divisors (factors): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 36, 40, 45, 48, 50, 54, 60, 72, 75, 80, 81, 90, 100, 108, 120, 135, 144, 150, 162, 180, 200, 216, 225, 240, 270, 300, 324, 360, 400, 405, 432, 450, 540, 600, 648, 675, 720, 810, 900, 1080, 1200, 1296, 1350, 1620, 1800, 2025, 2160, 2700, 3240, 3600, 4050, 5400, 6480, 8100, 10800, 16200, 32400.

Sum: 116281.  32400 is a perfect square (√32400 = 180).

Divisors (Factors) Calculator

Divisors Multiples Prime Factoriz. GCF LCM

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75 divisors
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 36, 40, 45, 48, 50, 54, 60, 72, 75, 80, 81, 90, 100, 108, 120, 135, 144, 150, 162, 180, 200, 216, 225, 240, 270, 300, 324, 360, 400, 405, 432, 450, 540, 600, 648, 675, 720, 810, 900, 1080, 1200, 1296, 1350, 1620, 1800, 2025, 2160, 2700, 3240, 3600, 4050, 5400, 6480, 8100, 10800, 16200, 32400

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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 32400

The number 32400 has 75 divisors:

1,  2,  3,  4,  5,  6,  8,  9,  10,  12,  15,  16,  18,  20,  24,  25,  27,  30,  36,  40,  45,  48,  50,  54,  60,  72,  75,  80,  81,  90,  100,  108,  120,  135,  144,  150,  162,  180,  200,  216,  225,  240,  270,  300,  324,  360,  400,  405,  432,  450,  540,  600,  648,  675,  720,  810,  900,  1080,  1200,  1296,  1350,  1620,  1800,  2025,  2160,  2700,  3240,  3600,  4050,  5400,  6480,  8100,  10800,  16200,  32400

Divisor Pairs of 32400

Each pair multiplies to 32400:

Factor 1×Factor 2=Product
1×32400=32400
2×16200=32400
3×10800=32400
4×8100=32400
5×6480=32400
6×5400=32400
8×4050=32400
9×3600=32400
10×3240=32400
12×2700=32400
15×2160=32400
16×2025=32400
18×1800=32400
20×1620=32400
24×1350=32400
25×1296=32400
27×1200=32400
30×1080=32400
36×900=32400
40×810=32400
45×720=32400
48×675=32400
50×648=32400
54×600=32400
60×540=32400
72×450=32400
75×432=32400
80×405=32400
81×400=32400
90×360=32400
100×324=32400
108×300=32400
120×270=32400
135×240=32400
144×225=32400
150×216=32400
162×200=32400
180×180=32400

Note: the last pair has identical factors (180 × 180) because 32400 is a perfect square.

Number of Divisors

The number 32400 has 75 divisors, written as τ(32400) = 75 in number theory.

⚡ Notice: 32400 has an odd number of divisors — this means 32400 is a perfect square (√32400 = 180).

Sum of Divisors

σ(32400) = 1 + 2 + 3 + 4 + 5 + 6 + 8 + 9 + 10 + 12 + 15 + 16 + 18 + 20 + 24 + 25 + 27 + 30 + 36 + 40 + 45 + 48 + 50 + 54 + 60 + 72 + 75 + 80 + 81 + 90 + 100 + 108 + 120 + 135 + 144 + 150 + 162 + 180 + 200 + 216 + 225 + 240 + 270 + 300 + 324 + 360 + 400 + 405 + 432 + 450 + 540 + 600 + 648 + 675 + 720 + 810 + 900 + 1080 + 1200 + 1296 + 1350 + 1620 + 1800 + 2025 + 2160 + 2700 + 3240 + 3600 + 4050 + 5400 + 6480 + 8100 + 10800 + 16200 + 32400 = 116281

Prime Factorization of 32400

See the full prime factorization calculator →

Properties of 32400

  • 32400 is composite.
  • 32400 is a perfect square (√32400 = 180).
  • Number of divisors: 75.
  • Sum of divisors: 116281.

Common Divisors with Another Number?

Looking for the divisors that 32400 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 32400

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √32400 ≈ 180.00. If i divides 32400, then both i and 32400/i are divisors.

  1. 1 divides 32400 (32400 ÷ 1 = 32400) → pair (1, 32400)
  2. 2 divides 32400 (32400 ÷ 2 = 16200) → pair (2, 16200)
  3. 3 divides 32400 (32400 ÷ 3 = 10800) → pair (3, 10800)
  4. 4 divides 32400 (32400 ÷ 4 = 8100) → pair (4, 8100)
  5. 5 divides 32400 (32400 ÷ 5 = 6480) → pair (5, 6480)
  6. 6 divides 32400 (32400 ÷ 6 = 5400) → pair (6, 5400)
  7. 8 divides 32400 (32400 ÷ 8 = 4050) → pair (8, 4050)
  8. 9 divides 32400 (32400 ÷ 9 = 3600) → pair (9, 3600)
  9. 10 divides 32400 (32400 ÷ 10 = 3240) → pair (10, 3240)
  10. 12 divides 32400 (32400 ÷ 12 = 2700) → pair (12, 2700)
  11. 15 divides 32400 (32400 ÷ 15 = 2160) → pair (15, 2160)
  12. 16 divides 32400 (32400 ÷ 16 = 2025) → pair (16, 2025)
  13. 18 divides 32400 (32400 ÷ 18 = 1800) → pair (18, 1800)
  14. 20 divides 32400 (32400 ÷ 20 = 1620) → pair (20, 1620)
  15. 24 divides 32400 (32400 ÷ 24 = 1350) → pair (24, 1350)
  16. 25 divides 32400 (32400 ÷ 25 = 1296) → pair (25, 1296)
  17. 27 divides 32400 (32400 ÷ 27 = 1200) → pair (27, 1200)
  18. 30 divides 32400 (32400 ÷ 30 = 1080) → pair (30, 1080)
  19. 36 divides 32400 (32400 ÷ 36 = 900) → pair (36, 900)
  20. 40 divides 32400 (32400 ÷ 40 = 810) → pair (40, 810)
  21. 45 divides 32400 (32400 ÷ 45 = 720) → pair (45, 720)
  22. 48 divides 32400 (32400 ÷ 48 = 675) → pair (48, 675)
  23. 50 divides 32400 (32400 ÷ 50 = 648) → pair (50, 648)
  24. 54 divides 32400 (32400 ÷ 54 = 600) → pair (54, 600)
  25. 60 divides 32400 (32400 ÷ 60 = 540) → pair (60, 540)
  26. 72 divides 32400 (32400 ÷ 72 = 450) → pair (72, 450)
  27. 75 divides 32400 (32400 ÷ 75 = 432) → pair (75, 432)
  28. 80 divides 32400 (32400 ÷ 80 = 405) → pair (80, 405)
  29. 81 divides 32400 (32400 ÷ 81 = 400) → pair (81, 400)
  30. 90 divides 32400 (32400 ÷ 90 = 360) → pair (90, 360)
  31. 100 divides 32400 (32400 ÷ 100 = 324) → pair (100, 324)
  32. 108 divides 32400 (32400 ÷ 108 = 300) → pair (108, 300)
  33. 120 divides 32400 (32400 ÷ 120 = 270) → pair (120, 270)
  34. 135 divides 32400 (32400 ÷ 135 = 240) → pair (135, 240)
  35. 144 divides 32400 (32400 ÷ 144 = 225) → pair (144, 225)
  36. 150 divides 32400 (32400 ÷ 150 = 216) → pair (150, 216)
  37. 162 divides 32400 (32400 ÷ 162 = 200) → pair (162, 200)
  38. 180 divides 32400 (32400 ÷ 180 = 180) → pair (180, 180)
  39. Collect all unique values: {1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 36, 40, 45, 48, 50, 54, 60, 72, 75, 80, 81, 90, 100, 108, 120, 135, 144, 150, 162, 180, 200, 216, 225, 240, 270, 300, 324, 360, 400, 405, 432, 450, 540, 600, 648, 675, 720, 810, 900, 1080, 1200, 1296, 1350, 1620, 1800, 2025, 2160, 2700, 3240, 3600, 4050, 5400, 6480, 8100, 10800, 16200, 32400} — total 75 divisors.
  40. Sum: 1 + 2 + 3 + 4 + 5 + 6 + 8 + 9 + 10 + 12 + 15 + 16 + 18 + 20 + 24 + 25 + 27 + 30 + 36 + 40 + 45 + 48 + 50 + 54 + 60 + 72 + 75 + 80 + 81 + 90 + 100 + 108 + 120 + 135 + 144 + 150 + 162 + 180 + 200 + 216 + 225 + 240 + 270 + 300 + 324 + 360 + 400 + 405 + 432 + 450 + 540 + 600 + 648 + 675 + 720 + 810 + 900 + 1080 + 1200 + 1296 + 1350 + 1620 + 1800 + 2025 + 2160 + 2700 + 3240 + 3600 + 4050 + 5400 + 6480 + 8100 + 10800 + 16200 + 32400 = 116281.

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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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