Divisors of 30240: 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 30240

The number 30240 has 96 divisors:

1,  2,  3,  4,  5,  6,  7,  8,  9,  10,  12,  14,  15,  16,  18,  20,  21,  24,  27,  28,  30,  32,  35,  36,  40,  42,  45,  48,  54,  56,  60,  63,  70,  72,  80,  84,  90,  96,  105,  108,  112,  120,  126,  135,  140,  144,  160,  168,  180,  189,  210,  216,  224,  240,  252,  270,  280,  288,  315,  336,  360,  378,  420,  432,  480,  504,  540,  560,  630,  672,  720,  756,  840,  864,  945,  1008,  1080,  1120,  1260,  1440,  1512,  1680,  1890,  2016,  2160,  2520,  3024,  3360,  3780,  4320,  5040,  6048,  7560,  10080,  15120,  30240

Divisor Pairs of 30240

Each pair multiplies to 30240:

Number of Divisors

The number 30240 has 96 divisors, written as τ(30240) = 96 in number theory.

Sum of Divisors

σ(30240) = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 12 + 14 + 15 + 16 + 18 + 20 + 21 + 24 + 27 + 28 + 30 + 32 + 35 + 36 + 40 + 42 + 45 + 48 + 54 + 56 + 60 + 63 + 70 + 72 + 80 + 84 + 90 + 96 + 105 + 108 + 112 + 120 + 126 + 135 + 140 + 144 + 160 + 168 + 180 + 189 + 210 + 216 + 224 + 240 + 252 + 270 + 280 + 288 + 315 + 336 + 360 + 378 + 420 + 432 + 480 + 504 + 540 + 560 + 630 + 672 + 720 + 756 + 840 + 864 + 945 + 1008 + 1080 + 1120 + 1260 + 1440 + 1512 + 1680 + 1890 + 2016 + 2160 + 2520 + 3024 + 3360 + 3780 + 4320 + 5040 + 6048 + 7560 + 10080 + 15120 + 30240 = 120960

Prime Factorization of 30240

See the full prime factorization calculator →

Properties of 30240

• 30240 is composite.
• 30240 is not a perfect square.
• Number of divisors: 96.
• Sum of divisors: 120960.

Common Divisors with Another Number?

Looking for the divisors that 30240 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 30240

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √30240 ≈ 173.90. If i divides 30240, then both i and 30240/i are divisors.

1. 1 divides 30240 (30240 ÷ 1 = 30240) → pair (1, 30240)
2. 2 divides 30240 (30240 ÷ 2 = 15120) → pair (2, 15120)
3. 3 divides 30240 (30240 ÷ 3 = 10080) → pair (3, 10080)
4. 4 divides 30240 (30240 ÷ 4 = 7560) → pair (4, 7560)
5. 5 divides 30240 (30240 ÷ 5 = 6048) → pair (5, 6048)
6. 6 divides 30240 (30240 ÷ 6 = 5040) → pair (6, 5040)
7. 7 divides 30240 (30240 ÷ 7 = 4320) → pair (7, 4320)
8. 8 divides 30240 (30240 ÷ 8 = 3780) → pair (8, 3780)
9. 9 divides 30240 (30240 ÷ 9 = 3360) → pair (9, 3360)
10. 10 divides 30240 (30240 ÷ 10 = 3024) → pair (10, 3024)
11. 12 divides 30240 (30240 ÷ 12 = 2520) → pair (12, 2520)
12. 14 divides 30240 (30240 ÷ 14 = 2160) → pair (14, 2160)
13. 15 divides 30240 (30240 ÷ 15 = 2016) → pair (15, 2016)
14. 16 divides 30240 (30240 ÷ 16 = 1890) → pair (16, 1890)
15. 18 divides 30240 (30240 ÷ 18 = 1680) → pair (18, 1680)
16. 20 divides 30240 (30240 ÷ 20 = 1512) → pair (20, 1512)
17. 21 divides 30240 (30240 ÷ 21 = 1440) → pair (21, 1440)
18. 24 divides 30240 (30240 ÷ 24 = 1260) → pair (24, 1260)
19. 27 divides 30240 (30240 ÷ 27 = 1120) → pair (27, 1120)
20. 28 divides 30240 (30240 ÷ 28 = 1080) → pair (28, 1080)
21. 30 divides 30240 (30240 ÷ 30 = 1008) → pair (30, 1008)
22. 32 divides 30240 (30240 ÷ 32 = 945) → pair (32, 945)
23. 35 divides 30240 (30240 ÷ 35 = 864) → pair (35, 864)
24. 36 divides 30240 (30240 ÷ 36 = 840) → pair (36, 840)
25. 40 divides 30240 (30240 ÷ 40 = 756) → pair (40, 756)
26. 42 divides 30240 (30240 ÷ 42 = 720) → pair (42, 720)
27. 45 divides 30240 (30240 ÷ 45 = 672) → pair (45, 672)
28. 48 divides 30240 (30240 ÷ 48 = 630) → pair (48, 630)
29. 54 divides 30240 (30240 ÷ 54 = 560) → pair (54, 560)
30. 56 divides 30240 (30240 ÷ 56 = 540) → pair (56, 540)
31. 60 divides 30240 (30240 ÷ 60 = 504) → pair (60, 504)
32. 63 divides 30240 (30240 ÷ 63 = 480) → pair (63, 480)
33. 70 divides 30240 (30240 ÷ 70 = 432) → pair (70, 432)
34. 72 divides 30240 (30240 ÷ 72 = 420) → pair (72, 420)
35. 80 divides 30240 (30240 ÷ 80 = 378) → pair (80, 378)
36. 84 divides 30240 (30240 ÷ 84 = 360) → pair (84, 360)
37. 90 divides 30240 (30240 ÷ 90 = 336) → pair (90, 336)
38. 96 divides 30240 (30240 ÷ 96 = 315) → pair (96, 315)
39. 105 divides 30240 (30240 ÷ 105 = 288) → pair (105, 288)
40. 108 divides 30240 (30240 ÷ 108 = 280) → pair (108, 280)
41. 112 divides 30240 (30240 ÷ 112 = 270) → pair (112, 270)
42. 120 divides 30240 (30240 ÷ 120 = 252) → pair (120, 252)
43. 126 divides 30240 (30240 ÷ 126 = 240) → pair (126, 240)
44. 135 divides 30240 (30240 ÷ 135 = 224) → pair (135, 224)
45. 140 divides 30240 (30240 ÷ 140 = 216) → pair (140, 216)
46. 144 divides 30240 (30240 ÷ 144 = 210) → pair (144, 210)
47. 160 divides 30240 (30240 ÷ 160 = 189) → pair (160, 189)
48. 168 divides 30240 (30240 ÷ 168 = 180) → pair (168, 180)
49. Collect all unique values: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 27, 28, 30, 32, 35, 36, 40, 42, 45, 48, 54, 56, 60, 63, 70, 72, 80, 84, 90, 96, 105, 108, 112, 120, 126, 135, 140, 144, 160, 168, 180, 189, 210, 216, 224, 240, 252, 270, 280, 288, 315, 336, 360, 378, 420, 432, 480, 504, 540, 560, 630, 672, 720, 756, 840, 864, 945, 1008, 1080, 1120, 1260, 1440, 1512, 1680, 1890, 2016, 2160, 2520, 3024, 3360, 3780, 4320, 5040, 6048, 7560, 10080, 15120, 30240} — total 96 divisors.
50. Sum: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 12 + 14 + 15 + 16 + 18 + 20 + 21 + 24 + 27 + 28 + 30 + 32 + 35 + 36 + 40 + 42 + 45 + 48 + 54 + 56 + 60 + 63 + 70 + 72 + 80 + 84 + 90 + 96 + 105 + 108 + 112 + 120 + 126 + 135 + 140 + 144 + 160 + 168 + 180 + 189 + 210 + 216 + 224 + 240 + 252 + 270 + 280 + 288 + 315 + 336 + 360 + 378 + 420 + 432 + 480 + 504 + 540 + 560 + 630 + 672 + 720 + 756 + 840 + 864 + 945 + 1008 + 1080 + 1120 + 1260 + 1440 + 1512 + 1680 + 1890 + 2016 + 2160 + 2520 + 3024 + 3360 + 3780 + 4320 + 5040 + 6048 + 7560 + 10080 + 15120 + 30240 = 120960.

Nearby Examples

Related Operations for 30240

• Multiples of a Number — "outward" complement of divisors
• 30240 Prime Factorization — decompose into prime building blocks
• Find GCF of 30240 and another number
• Find LCM of 30240 and another number
• Is 30240 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

Find all divisors of these numbers: