Divisors of 31200: All 72 Factors

Quick Answer

31200 has 72 divisors (factors): 1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 16, 20, 24, 25, 26, 30, 32, 39, 40, 48, 50, 52, 60, 65, 75, 78, 80, 96, 100, 104, 120, 130, 150, 156, 160, 195, 200, 208, 240, 260, 300, 312, 325, 390, 400, 416, 480, 520, 600, 624, 650, 780, 800, 975, 1040, 1200, 1248, 1300, 1560, 1950, 2080, 2400, 2600, 3120, 3900, 5200, 6240, 7800, 10400, 15600, 31200.

Sum: 109368.

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, 10, 12, 13, 15, 16, 20, 24, 25, 26, 30, 32, 39, 40, 48, 50, 52, 60, 65, 75, 78, 80, 96, 100, 104, 120, 130, 150, 156, 160, 195, 200, 208, 240, 260, 300, 312, 325, 390, 400, 416, 480, 520, 600, 624, 650, 780, 800, 975, 1040, 1200, 1248, 1300, 1560, 1950, 2080, 2400, 2600, 3120, 3900, 5200, 6240, 7800, 10400, 15600, 31200

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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 31200

The number 31200 has 72 divisors:

1,  2,  3,  4,  5,  6,  8,  10,  12,  13,  15,  16,  20,  24,  25,  26,  30,  32,  39,  40,  48,  50,  52,  60,  65,  75,  78,  80,  96,  100,  104,  120,  130,  150,  156,  160,  195,  200,  208,  240,  260,  300,  312,  325,  390,  400,  416,  480,  520,  600,  624,  650,  780,  800,  975,  1040,  1200,  1248,  1300,  1560,  1950,  2080,  2400,  2600,  3120,  3900,  5200,  6240,  7800,  10400,  15600,  31200

Divisor Pairs of 31200

Each pair multiplies to 31200:

Factor 1×Factor 2=Product
1×31200=31200
2×15600=31200
3×10400=31200
4×7800=31200
5×6240=31200
6×5200=31200
8×3900=31200
10×3120=31200
12×2600=31200
13×2400=31200
15×2080=31200
16×1950=31200
20×1560=31200
24×1300=31200
25×1248=31200
26×1200=31200
30×1040=31200
32×975=31200
39×800=31200
40×780=31200
48×650=31200
50×624=31200
52×600=31200
60×520=31200
65×480=31200
75×416=31200
78×400=31200
80×390=31200
96×325=31200
100×312=31200
104×300=31200
120×260=31200
130×240=31200
150×208=31200
156×200=31200
160×195=31200

Number of Divisors

The number 31200 has 72 divisors, written as τ(31200) = 72 in number theory.

Sum of Divisors

σ(31200) = 1 + 2 + 3 + 4 + 5 + 6 + 8 + 10 + 12 + 13 + 15 + 16 + 20 + 24 + 25 + 26 + 30 + 32 + 39 + 40 + 48 + 50 + 52 + 60 + 65 + 75 + 78 + 80 + 96 + 100 + 104 + 120 + 130 + 150 + 156 + 160 + 195 + 200 + 208 + 240 + 260 + 300 + 312 + 325 + 390 + 400 + 416 + 480 + 520 + 600 + 624 + 650 + 780 + 800 + 975 + 1040 + 1200 + 1248 + 1300 + 1560 + 1950 + 2080 + 2400 + 2600 + 3120 + 3900 + 5200 + 6240 + 7800 + 10400 + 15600 + 31200 = 109368

Prime Factorization of 31200

See the full prime factorization calculator →

Properties of 31200

  • 31200 is composite.
  • 31200 is not a perfect square.
  • Number of divisors: 72.
  • Sum of divisors: 109368.

Common Divisors with Another Number?

Looking for the divisors that 31200 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 31200

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √31200 ≈ 176.64. If i divides 31200, then both i and 31200/i are divisors.

  1. 1 divides 31200 (31200 ÷ 1 = 31200) → pair (1, 31200)
  2. 2 divides 31200 (31200 ÷ 2 = 15600) → pair (2, 15600)
  3. 3 divides 31200 (31200 ÷ 3 = 10400) → pair (3, 10400)
  4. 4 divides 31200 (31200 ÷ 4 = 7800) → pair (4, 7800)
  5. 5 divides 31200 (31200 ÷ 5 = 6240) → pair (5, 6240)
  6. 6 divides 31200 (31200 ÷ 6 = 5200) → pair (6, 5200)
  7. 8 divides 31200 (31200 ÷ 8 = 3900) → pair (8, 3900)
  8. 10 divides 31200 (31200 ÷ 10 = 3120) → pair (10, 3120)
  9. 12 divides 31200 (31200 ÷ 12 = 2600) → pair (12, 2600)
  10. 13 divides 31200 (31200 ÷ 13 = 2400) → pair (13, 2400)
  11. 15 divides 31200 (31200 ÷ 15 = 2080) → pair (15, 2080)
  12. 16 divides 31200 (31200 ÷ 16 = 1950) → pair (16, 1950)
  13. 20 divides 31200 (31200 ÷ 20 = 1560) → pair (20, 1560)
  14. 24 divides 31200 (31200 ÷ 24 = 1300) → pair (24, 1300)
  15. 25 divides 31200 (31200 ÷ 25 = 1248) → pair (25, 1248)
  16. 26 divides 31200 (31200 ÷ 26 = 1200) → pair (26, 1200)
  17. 30 divides 31200 (31200 ÷ 30 = 1040) → pair (30, 1040)
  18. 32 divides 31200 (31200 ÷ 32 = 975) → pair (32, 975)
  19. 39 divides 31200 (31200 ÷ 39 = 800) → pair (39, 800)
  20. 40 divides 31200 (31200 ÷ 40 = 780) → pair (40, 780)
  21. 48 divides 31200 (31200 ÷ 48 = 650) → pair (48, 650)
  22. 50 divides 31200 (31200 ÷ 50 = 624) → pair (50, 624)
  23. 52 divides 31200 (31200 ÷ 52 = 600) → pair (52, 600)
  24. 60 divides 31200 (31200 ÷ 60 = 520) → pair (60, 520)
  25. 65 divides 31200 (31200 ÷ 65 = 480) → pair (65, 480)
  26. 75 divides 31200 (31200 ÷ 75 = 416) → pair (75, 416)
  27. 78 divides 31200 (31200 ÷ 78 = 400) → pair (78, 400)
  28. 80 divides 31200 (31200 ÷ 80 = 390) → pair (80, 390)
  29. 96 divides 31200 (31200 ÷ 96 = 325) → pair (96, 325)
  30. 100 divides 31200 (31200 ÷ 100 = 312) → pair (100, 312)
  31. 104 divides 31200 (31200 ÷ 104 = 300) → pair (104, 300)
  32. 120 divides 31200 (31200 ÷ 120 = 260) → pair (120, 260)
  33. 130 divides 31200 (31200 ÷ 130 = 240) → pair (130, 240)
  34. 150 divides 31200 (31200 ÷ 150 = 208) → pair (150, 208)
  35. 156 divides 31200 (31200 ÷ 156 = 200) → pair (156, 200)
  36. 160 divides 31200 (31200 ÷ 160 = 195) → pair (160, 195)
  37. Collect all unique values: {1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 16, 20, 24, 25, 26, 30, 32, 39, 40, 48, 50, 52, 60, 65, 75, 78, 80, 96, 100, 104, 120, 130, 150, 156, 160, 195, 200, 208, 240, 260, 300, 312, 325, 390, 400, 416, 480, 520, 600, 624, 650, 780, 800, 975, 1040, 1200, 1248, 1300, 1560, 1950, 2080, 2400, 2600, 3120, 3900, 5200, 6240, 7800, 10400, 15600, 31200} — total 72 divisors.
  38. Sum: 1 + 2 + 3 + 4 + 5 + 6 + 8 + 10 + 12 + 13 + 15 + 16 + 20 + 24 + 25 + 26 + 30 + 32 + 39 + 40 + 48 + 50 + 52 + 60 + 65 + 75 + 78 + 80 + 96 + 100 + 104 + 120 + 130 + 150 + 156 + 160 + 195 + 200 + 208 + 240 + 260 + 300 + 312 + 325 + 390 + 400 + 416 + 480 + 520 + 600 + 624 + 650 + 780 + 800 + 975 + 1040 + 1200 + 1248 + 1300 + 1560 + 1950 + 2080 + 2400 + 2600 + 3120 + 3900 + 5200 + 6240 + 7800 + 10400 + 15600 + 31200 = 109368.

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Related Operations for 31200

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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