Divisors of 67200: All 96 Factors

Divisors (Factors) Calculator

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 67200

The number 67200 has 96 divisors:

1,  2,  3,  4,  5,  6,  7,  8,  10,  12,  14,  15,  16,  20,  21,  24,  25,  28,  30,  32,  35,  40,  42,  48,  50,  56,  60,  64,  70,  75,  80,  84,  96,  100,  105,  112,  120,  128,  140,  150,  160,  168,  175,  192,  200,  210,  224,  240,  280,  300,  320,  336,  350,  384,  400,  420,  448,  480,  525,  560,  600,  640,  672,  700,  800,  840,  896,  960,  1050,  1120,  1200,  1344,  1400,  1600,  1680,  1920,  2100,  2240,  2400,  2688,  2800,  3200,  3360,  4200,  4480,  4800,  5600,  6720,  8400,  9600,  11200,  13440,  16800,  22400,  33600,  67200

Divisor Pairs of 67200

Each pair multiplies to 67200:

Number of Divisors

The number 67200 has 96 divisors, written as τ(67200) = 96 in number theory.

Sum of Divisors

σ(67200) = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 10 + 12 + 14 + 15 + 16 + 20 + 21 + 24 + 25 + 28 + 30 + 32 + 35 + 40 + 42 + 48 + 50 + 56 + 60 + 64 + 70 + 75 + 80 + 84 + 96 + 100 + 105 + 112 + 120 + 128 + 140 + 150 + 160 + 168 + 175 + 192 + 200 + 210 + 224 + 240 + 280 + 300 + 320 + 336 + 350 + 384 + 400 + 420 + 448 + 480 + 525 + 560 + 600 + 640 + 672 + 700 + 800 + 840 + 896 + 960 + 1050 + 1120 + 1200 + 1344 + 1400 + 1600 + 1680 + 1920 + 2100 + 2240 + 2400 + 2688 + 2800 + 3200 + 3360 + 4200 + 4480 + 4800 + 5600 + 6720 + 8400 + 9600 + 11200 + 13440 + 16800 + 22400 + 33600 + 67200 = 252960

Prime Factorization of 67200

See the full prime factorization calculator →

Properties of 67200

• 67200 is composite.
• 67200 is not a perfect square.
• Number of divisors: 96.
• Sum of divisors: 252960.

Common Divisors with Another Number?

Looking for the divisors that 67200 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 67200

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √67200 ≈ 259.23. If i divides 67200, then both i and 67200/i are divisors.

1. 1 divides 67200 (67200 ÷ 1 = 67200) → pair (1, 67200)
2. 2 divides 67200 (67200 ÷ 2 = 33600) → pair (2, 33600)
3. 3 divides 67200 (67200 ÷ 3 = 22400) → pair (3, 22400)
4. 4 divides 67200 (67200 ÷ 4 = 16800) → pair (4, 16800)
5. 5 divides 67200 (67200 ÷ 5 = 13440) → pair (5, 13440)
6. 6 divides 67200 (67200 ÷ 6 = 11200) → pair (6, 11200)
7. 7 divides 67200 (67200 ÷ 7 = 9600) → pair (7, 9600)
8. 8 divides 67200 (67200 ÷ 8 = 8400) → pair (8, 8400)
9. 10 divides 67200 (67200 ÷ 10 = 6720) → pair (10, 6720)
10. 12 divides 67200 (67200 ÷ 12 = 5600) → pair (12, 5600)
11. 14 divides 67200 (67200 ÷ 14 = 4800) → pair (14, 4800)
12. 15 divides 67200 (67200 ÷ 15 = 4480) → pair (15, 4480)
13. 16 divides 67200 (67200 ÷ 16 = 4200) → pair (16, 4200)
14. 20 divides 67200 (67200 ÷ 20 = 3360) → pair (20, 3360)
15. 21 divides 67200 (67200 ÷ 21 = 3200) → pair (21, 3200)
16. 24 divides 67200 (67200 ÷ 24 = 2800) → pair (24, 2800)
17. 25 divides 67200 (67200 ÷ 25 = 2688) → pair (25, 2688)
18. 28 divides 67200 (67200 ÷ 28 = 2400) → pair (28, 2400)
19. 30 divides 67200 (67200 ÷ 30 = 2240) → pair (30, 2240)
20. 32 divides 67200 (67200 ÷ 32 = 2100) → pair (32, 2100)
21. 35 divides 67200 (67200 ÷ 35 = 1920) → pair (35, 1920)
22. 40 divides 67200 (67200 ÷ 40 = 1680) → pair (40, 1680)
23. 42 divides 67200 (67200 ÷ 42 = 1600) → pair (42, 1600)
24. 48 divides 67200 (67200 ÷ 48 = 1400) → pair (48, 1400)
25. 50 divides 67200 (67200 ÷ 50 = 1344) → pair (50, 1344)
26. 56 divides 67200 (67200 ÷ 56 = 1200) → pair (56, 1200)
27. 60 divides 67200 (67200 ÷ 60 = 1120) → pair (60, 1120)
28. 64 divides 67200 (67200 ÷ 64 = 1050) → pair (64, 1050)
29. 70 divides 67200 (67200 ÷ 70 = 960) → pair (70, 960)
30. 75 divides 67200 (67200 ÷ 75 = 896) → pair (75, 896)
31. 80 divides 67200 (67200 ÷ 80 = 840) → pair (80, 840)
32. 84 divides 67200 (67200 ÷ 84 = 800) → pair (84, 800)
33. 96 divides 67200 (67200 ÷ 96 = 700) → pair (96, 700)
34. 100 divides 67200 (67200 ÷ 100 = 672) → pair (100, 672)
35. 105 divides 67200 (67200 ÷ 105 = 640) → pair (105, 640)
36. 112 divides 67200 (67200 ÷ 112 = 600) → pair (112, 600)
37. 120 divides 67200 (67200 ÷ 120 = 560) → pair (120, 560)
38. 128 divides 67200 (67200 ÷ 128 = 525) → pair (128, 525)
39. 140 divides 67200 (67200 ÷ 140 = 480) → pair (140, 480)
40. 150 divides 67200 (67200 ÷ 150 = 448) → pair (150, 448)
41. 160 divides 67200 (67200 ÷ 160 = 420) → pair (160, 420)
42. 168 divides 67200 (67200 ÷ 168 = 400) → pair (168, 400)
43. 175 divides 67200 (67200 ÷ 175 = 384) → pair (175, 384)
44. 192 divides 67200 (67200 ÷ 192 = 350) → pair (192, 350)
45. 200 divides 67200 (67200 ÷ 200 = 336) → pair (200, 336)
46. 210 divides 67200 (67200 ÷ 210 = 320) → pair (210, 320)
47. 224 divides 67200 (67200 ÷ 224 = 300) → pair (224, 300)
48. 240 divides 67200 (67200 ÷ 240 = 280) → pair (240, 280)
49. Collect all unique values: {1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 25, 28, 30, 32, 35, 40, 42, 48, 50, 56, 60, 64, 70, 75, 80, 84, 96, 100, 105, 112, 120, 128, 140, 150, 160, 168, 175, 192, 200, 210, 224, 240, 280, 300, 320, 336, 350, 384, 400, 420, 448, 480, 525, 560, 600, 640, 672, 700, 800, 840, 896, 960, 1050, 1120, 1200, 1344, 1400, 1600, 1680, 1920, 2100, 2240, 2400, 2688, 2800, 3200, 3360, 4200, 4480, 4800, 5600, 6720, 8400, 9600, 11200, 13440, 16800, 22400, 33600, 67200} — total 96 divisors.
50. Sum: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 10 + 12 + 14 + 15 + 16 + 20 + 21 + 24 + 25 + 28 + 30 + 32 + 35 + 40 + 42 + 48 + 50 + 56 + 60 + 64 + 70 + 75 + 80 + 84 + 96 + 100 + 105 + 112 + 120 + 128 + 140 + 150 + 160 + 168 + 175 + 192 + 200 + 210 + 224 + 240 + 280 + 300 + 320 + 336 + 350 + 384 + 400 + 420 + 448 + 480 + 525 + 560 + 600 + 640 + 672 + 700 + 800 + 840 + 896 + 960 + 1050 + 1120 + 1200 + 1344 + 1400 + 1600 + 1680 + 1920 + 2100 + 2240 + 2400 + 2688 + 2800 + 3200 + 3360 + 4200 + 4480 + 4800 + 5600 + 6720 + 8400 + 9600 + 11200 + 13440 + 16800 + 22400 + 33600 + 67200 = 252960.

Nearby Examples

Related Operations for 67200

• Multiples of a Number — "outward" complement of divisors
• 67200 Prime Factorization — decompose into prime building blocks
• Find GCF of 67200 and another number
• Find LCM of 67200 and another number
• Is 67200 a perfect square? (odd divisor count ⇔ yes)

See also our tables of divisors:

• Table of all divisors from 1 to 100
• Table of all divisors from 1 to 500
• Table of all divisors from 1 to 1,000
• Table of all divisors from 1 to 10,000

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

• [1] Divisor (Wikipedia)
• [2] Divisor function (Wikipedia)
• [3] Divisor (Wolfram MathWorld)

Divisors Calculation Examples

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