Divisors of 42000: All 80 Factors

Quick Answer

42000 has 80 divisors (factors): 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 25, 28, 30, 35, 40, 42, 48, 50, 56, 60, 70, 75, 80, 84, 100, 105, 112, 120, 125, 140, 150, 168, 175, 200, 210, 240, 250, 280, 300, 336, 350, 375, 400, 420, 500, 525, 560, 600, 700, 750, 840, 875, 1000, 1050, 1200, 1400, 1500, 1680, 1750, 2000, 2100, 2625, 2800, 3000, 3500, 4200, 5250, 6000, 7000, 8400, 10500, 14000, 21000, 42000.

Sum: 154752.

Divisors (Factors) Calculator

Divisors Multiples Prime Factoriz. GCF LCM

  Ex.: 12, 36, 100, 1024, 1728, etc.
80 divisors
1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 25, 28, 30, 35, 40, 42, 48, 50, 56, 60, 70, 75, 80, 84, 100, 105, 112, 120, 125, 140, 150, 168, 175, 200, 210, 240, 250, 280, 300, 336, 350, 375, 400, 420, 500, 525, 560, 600, 700, 750, 840, 875, 1000, 1050, 1200, 1400, 1500, 1680, 1750, 2000, 2100, 2625, 2800, 3000, 3500, 4200, 5250, 6000, 7000, 8400, 10500, 14000, 21000, 42000

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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 42000

The number 42000 has 80 divisors:

1,  2,  3,  4,  5,  6,  7,  8,  10,  12,  14,  15,  16,  20,  21,  24,  25,  28,  30,  35,  40,  42,  48,  50,  56,  60,  70,  75,  80,  84,  100,  105,  112,  120,  125,  140,  150,  168,  175,  200,  210,  240,  250,  280,  300,  336,  350,  375,  400,  420,  500,  525,  560,  600,  700,  750,  840,  875,  1000,  1050,  1200,  1400,  1500,  1680,  1750,  2000,  2100,  2625,  2800,  3000,  3500,  4200,  5250,  6000,  7000,  8400,  10500,  14000,  21000,  42000

Divisor Pairs of 42000

Each pair multiplies to 42000:

Factor 1×Factor 2=Product
1×42000=42000
2×21000=42000
3×14000=42000
4×10500=42000
5×8400=42000
6×7000=42000
7×6000=42000
8×5250=42000
10×4200=42000
12×3500=42000
14×3000=42000
15×2800=42000
16×2625=42000
20×2100=42000
21×2000=42000
24×1750=42000
25×1680=42000
28×1500=42000
30×1400=42000
35×1200=42000
40×1050=42000
42×1000=42000
48×875=42000
50×840=42000
56×750=42000
60×700=42000
70×600=42000
75×560=42000
80×525=42000
84×500=42000
100×420=42000
105×400=42000
112×375=42000
120×350=42000
125×336=42000
140×300=42000
150×280=42000
168×250=42000
175×240=42000
200×210=42000

Number of Divisors

The number 42000 has 80 divisors, written as τ(42000) = 80 in number theory.

Sum of Divisors

σ(42000) = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 10 + 12 + 14 + 15 + 16 + 20 + 21 + 24 + 25 + 28 + 30 + 35 + 40 + 42 + 48 + 50 + 56 + 60 + 70 + 75 + 80 + 84 + 100 + 105 + 112 + 120 + 125 + 140 + 150 + 168 + 175 + 200 + 210 + 240 + 250 + 280 + 300 + 336 + 350 + 375 + 400 + 420 + 500 + 525 + 560 + 600 + 700 + 750 + 840 + 875 + 1000 + 1050 + 1200 + 1400 + 1500 + 1680 + 1750 + 2000 + 2100 + 2625 + 2800 + 3000 + 3500 + 4200 + 5250 + 6000 + 7000 + 8400 + 10500 + 14000 + 21000 + 42000 = 154752

Prime Factorization of 42000

See the full prime factorization calculator →

Properties of 42000

  • 42000 is composite.
  • 42000 is not a perfect square.
  • Number of divisors: 80.
  • Sum of divisors: 154752.

Common Divisors with Another Number?

Looking for the divisors that 42000 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 42000

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √42000 ≈ 204.94. If i divides 42000, then both i and 42000/i are divisors.

  1. 1 divides 42000 (42000 ÷ 1 = 42000) → pair (1, 42000)
  2. 2 divides 42000 (42000 ÷ 2 = 21000) → pair (2, 21000)
  3. 3 divides 42000 (42000 ÷ 3 = 14000) → pair (3, 14000)
  4. 4 divides 42000 (42000 ÷ 4 = 10500) → pair (4, 10500)
  5. 5 divides 42000 (42000 ÷ 5 = 8400) → pair (5, 8400)
  6. 6 divides 42000 (42000 ÷ 6 = 7000) → pair (6, 7000)
  7. 7 divides 42000 (42000 ÷ 7 = 6000) → pair (7, 6000)
  8. 8 divides 42000 (42000 ÷ 8 = 5250) → pair (8, 5250)
  9. 10 divides 42000 (42000 ÷ 10 = 4200) → pair (10, 4200)
  10. 12 divides 42000 (42000 ÷ 12 = 3500) → pair (12, 3500)
  11. 14 divides 42000 (42000 ÷ 14 = 3000) → pair (14, 3000)
  12. 15 divides 42000 (42000 ÷ 15 = 2800) → pair (15, 2800)
  13. 16 divides 42000 (42000 ÷ 16 = 2625) → pair (16, 2625)
  14. 20 divides 42000 (42000 ÷ 20 = 2100) → pair (20, 2100)
  15. 21 divides 42000 (42000 ÷ 21 = 2000) → pair (21, 2000)
  16. 24 divides 42000 (42000 ÷ 24 = 1750) → pair (24, 1750)
  17. 25 divides 42000 (42000 ÷ 25 = 1680) → pair (25, 1680)
  18. 28 divides 42000 (42000 ÷ 28 = 1500) → pair (28, 1500)
  19. 30 divides 42000 (42000 ÷ 30 = 1400) → pair (30, 1400)
  20. 35 divides 42000 (42000 ÷ 35 = 1200) → pair (35, 1200)
  21. 40 divides 42000 (42000 ÷ 40 = 1050) → pair (40, 1050)
  22. 42 divides 42000 (42000 ÷ 42 = 1000) → pair (42, 1000)
  23. 48 divides 42000 (42000 ÷ 48 = 875) → pair (48, 875)
  24. 50 divides 42000 (42000 ÷ 50 = 840) → pair (50, 840)
  25. 56 divides 42000 (42000 ÷ 56 = 750) → pair (56, 750)
  26. 60 divides 42000 (42000 ÷ 60 = 700) → pair (60, 700)
  27. 70 divides 42000 (42000 ÷ 70 = 600) → pair (70, 600)
  28. 75 divides 42000 (42000 ÷ 75 = 560) → pair (75, 560)
  29. 80 divides 42000 (42000 ÷ 80 = 525) → pair (80, 525)
  30. 84 divides 42000 (42000 ÷ 84 = 500) → pair (84, 500)
  31. 100 divides 42000 (42000 ÷ 100 = 420) → pair (100, 420)
  32. 105 divides 42000 (42000 ÷ 105 = 400) → pair (105, 400)
  33. 112 divides 42000 (42000 ÷ 112 = 375) → pair (112, 375)
  34. 120 divides 42000 (42000 ÷ 120 = 350) → pair (120, 350)
  35. 125 divides 42000 (42000 ÷ 125 = 336) → pair (125, 336)
  36. 140 divides 42000 (42000 ÷ 140 = 300) → pair (140, 300)
  37. 150 divides 42000 (42000 ÷ 150 = 280) → pair (150, 280)
  38. 168 divides 42000 (42000 ÷ 168 = 250) → pair (168, 250)
  39. 175 divides 42000 (42000 ÷ 175 = 240) → pair (175, 240)
  40. 200 divides 42000 (42000 ÷ 200 = 210) → pair (200, 210)
  41. Collect all unique values: {1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 25, 28, 30, 35, 40, 42, 48, 50, 56, 60, 70, 75, 80, 84, 100, 105, 112, 120, 125, 140, 150, 168, 175, 200, 210, 240, 250, 280, 300, 336, 350, 375, 400, 420, 500, 525, 560, 600, 700, 750, 840, 875, 1000, 1050, 1200, 1400, 1500, 1680, 1750, 2000, 2100, 2625, 2800, 3000, 3500, 4200, 5250, 6000, 7000, 8400, 10500, 14000, 21000, 42000} — total 80 divisors.
  42. Sum: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 10 + 12 + 14 + 15 + 16 + 20 + 21 + 24 + 25 + 28 + 30 + 35 + 40 + 42 + 48 + 50 + 56 + 60 + 70 + 75 + 80 + 84 + 100 + 105 + 112 + 120 + 125 + 140 + 150 + 168 + 175 + 200 + 210 + 240 + 250 + 280 + 300 + 336 + 350 + 375 + 400 + 420 + 500 + 525 + 560 + 600 + 700 + 750 + 840 + 875 + 1000 + 1050 + 1200 + 1400 + 1500 + 1680 + 1750 + 2000 + 2100 + 2625 + 2800 + 3000 + 3500 + 4200 + 5250 + 6000 + 7000 + 8400 + 10500 + 14000 + 21000 + 42000 = 154752.

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Related Operations for 42000

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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