Divisors of 77280: 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 77280

The number 77280 has 96 divisors:

1,  2,  3,  4,  5,  6,  7,  8,  10,  12,  14,  15,  16,  20,  21,  23,  24,  28,  30,  32,  35,  40,  42,  46,  48,  56,  60,  69,  70,  80,  84,  92,  96,  105,  112,  115,  120,  138,  140,  160,  161,  168,  184,  210,  224,  230,  240,  276,  280,  322,  336,  345,  368,  420,  460,  480,  483,  552,  560,  644,  672,  690,  736,  805,  840,  920,  966,  1104,  1120,  1288,  1380,  1610,  1680,  1840,  1932,  2208,  2415,  2576,  2760,  3220,  3360,  3680,  3864,  4830,  5152,  5520,  6440,  7728,  9660,  11040,  12880,  15456,  19320,  25760,  38640,  77280

Divisor Pairs of 77280

Each pair multiplies to 77280:

Number of Divisors

The number 77280 has 96 divisors, written as τ(77280) = 96 in number theory.

Sum of Divisors

σ(77280) = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 10 + 12 + 14 + 15 + 16 + 20 + 21 + 23 + 24 + 28 + 30 + 32 + 35 + 40 + 42 + 46 + 48 + 56 + 60 + 69 + 70 + 80 + 84 + 92 + 96 + 105 + 112 + 115 + 120 + 138 + 140 + 160 + 161 + 168 + 184 + 210 + 224 + 230 + 240 + 276 + 280 + 322 + 336 + 345 + 368 + 420 + 460 + 480 + 483 + 552 + 560 + 644 + 672 + 690 + 736 + 805 + 840 + 920 + 966 + 1104 + 1120 + 1288 + 1380 + 1610 + 1680 + 1840 + 1932 + 2208 + 2415 + 2576 + 2760 + 3220 + 3360 + 3680 + 3864 + 4830 + 5152 + 5520 + 6440 + 7728 + 9660 + 11040 + 12880 + 15456 + 19320 + 25760 + 38640 + 77280 = 290304

Prime Factorization of 77280

See the full prime factorization calculator →

Properties of 77280

• 77280 is composite.
• 77280 is not a perfect square.
• Number of divisors: 96.
• Sum of divisors: 290304.

Common Divisors with Another Number?

Looking for the divisors that 77280 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 77280

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √77280 ≈ 277.99. If i divides 77280, then both i and 77280/i are divisors.

1. 1 divides 77280 (77280 ÷ 1 = 77280) → pair (1, 77280)
2. 2 divides 77280 (77280 ÷ 2 = 38640) → pair (2, 38640)
3. 3 divides 77280 (77280 ÷ 3 = 25760) → pair (3, 25760)
4. 4 divides 77280 (77280 ÷ 4 = 19320) → pair (4, 19320)
5. 5 divides 77280 (77280 ÷ 5 = 15456) → pair (5, 15456)
6. 6 divides 77280 (77280 ÷ 6 = 12880) → pair (6, 12880)
7. 7 divides 77280 (77280 ÷ 7 = 11040) → pair (7, 11040)
8. 8 divides 77280 (77280 ÷ 8 = 9660) → pair (8, 9660)
9. 10 divides 77280 (77280 ÷ 10 = 7728) → pair (10, 7728)
10. 12 divides 77280 (77280 ÷ 12 = 6440) → pair (12, 6440)
11. 14 divides 77280 (77280 ÷ 14 = 5520) → pair (14, 5520)
12. 15 divides 77280 (77280 ÷ 15 = 5152) → pair (15, 5152)
13. 16 divides 77280 (77280 ÷ 16 = 4830) → pair (16, 4830)
14. 20 divides 77280 (77280 ÷ 20 = 3864) → pair (20, 3864)
15. 21 divides 77280 (77280 ÷ 21 = 3680) → pair (21, 3680)
16. 23 divides 77280 (77280 ÷ 23 = 3360) → pair (23, 3360)
17. 24 divides 77280 (77280 ÷ 24 = 3220) → pair (24, 3220)
18. 28 divides 77280 (77280 ÷ 28 = 2760) → pair (28, 2760)
19. 30 divides 77280 (77280 ÷ 30 = 2576) → pair (30, 2576)
20. 32 divides 77280 (77280 ÷ 32 = 2415) → pair (32, 2415)
21. 35 divides 77280 (77280 ÷ 35 = 2208) → pair (35, 2208)
22. 40 divides 77280 (77280 ÷ 40 = 1932) → pair (40, 1932)
23. 42 divides 77280 (77280 ÷ 42 = 1840) → pair (42, 1840)
24. 46 divides 77280 (77280 ÷ 46 = 1680) → pair (46, 1680)
25. 48 divides 77280 (77280 ÷ 48 = 1610) → pair (48, 1610)
26. 56 divides 77280 (77280 ÷ 56 = 1380) → pair (56, 1380)
27. 60 divides 77280 (77280 ÷ 60 = 1288) → pair (60, 1288)
28. 69 divides 77280 (77280 ÷ 69 = 1120) → pair (69, 1120)
29. 70 divides 77280 (77280 ÷ 70 = 1104) → pair (70, 1104)
30. 80 divides 77280 (77280 ÷ 80 = 966) → pair (80, 966)
31. 84 divides 77280 (77280 ÷ 84 = 920) → pair (84, 920)
32. 92 divides 77280 (77280 ÷ 92 = 840) → pair (92, 840)
33. 96 divides 77280 (77280 ÷ 96 = 805) → pair (96, 805)
34. 105 divides 77280 (77280 ÷ 105 = 736) → pair (105, 736)
35. 112 divides 77280 (77280 ÷ 112 = 690) → pair (112, 690)
36. 115 divides 77280 (77280 ÷ 115 = 672) → pair (115, 672)
37. 120 divides 77280 (77280 ÷ 120 = 644) → pair (120, 644)
38. 138 divides 77280 (77280 ÷ 138 = 560) → pair (138, 560)
39. 140 divides 77280 (77280 ÷ 140 = 552) → pair (140, 552)
40. 160 divides 77280 (77280 ÷ 160 = 483) → pair (160, 483)
41. 161 divides 77280 (77280 ÷ 161 = 480) → pair (161, 480)
42. 168 divides 77280 (77280 ÷ 168 = 460) → pair (168, 460)
43. 184 divides 77280 (77280 ÷ 184 = 420) → pair (184, 420)
44. 210 divides 77280 (77280 ÷ 210 = 368) → pair (210, 368)
45. 224 divides 77280 (77280 ÷ 224 = 345) → pair (224, 345)
46. 230 divides 77280 (77280 ÷ 230 = 336) → pair (230, 336)
47. 240 divides 77280 (77280 ÷ 240 = 322) → pair (240, 322)
48. 276 divides 77280 (77280 ÷ 276 = 280) → pair (276, 280)
49. Collect all unique values: {1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 23, 24, 28, 30, 32, 35, 40, 42, 46, 48, 56, 60, 69, 70, 80, 84, 92, 96, 105, 112, 115, 120, 138, 140, 160, 161, 168, 184, 210, 224, 230, 240, 276, 280, 322, 336, 345, 368, 420, 460, 480, 483, 552, 560, 644, 672, 690, 736, 805, 840, 920, 966, 1104, 1120, 1288, 1380, 1610, 1680, 1840, 1932, 2208, 2415, 2576, 2760, 3220, 3360, 3680, 3864, 4830, 5152, 5520, 6440, 7728, 9660, 11040, 12880, 15456, 19320, 25760, 38640, 77280} — total 96 divisors.
50. Sum: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 10 + 12 + 14 + 15 + 16 + 20 + 21 + 23 + 24 + 28 + 30 + 32 + 35 + 40 + 42 + 46 + 48 + 56 + 60 + 69 + 70 + 80 + 84 + 92 + 96 + 105 + 112 + 115 + 120 + 138 + 140 + 160 + 161 + 168 + 184 + 210 + 224 + 230 + 240 + 276 + 280 + 322 + 336 + 345 + 368 + 420 + 460 + 480 + 483 + 552 + 560 + 644 + 672 + 690 + 736 + 805 + 840 + 920 + 966 + 1104 + 1120 + 1288 + 1380 + 1610 + 1680 + 1840 + 1932 + 2208 + 2415 + 2576 + 2760 + 3220 + 3360 + 3680 + 3864 + 4830 + 5152 + 5520 + 6440 + 7728 + 9660 + 11040 + 12880 + 15456 + 19320 + 25760 + 38640 + 77280 = 290304.

Nearby Examples

Related Operations for 77280

• Multiples of a Number — "outward" complement of divisors
• 77280 Prime Factorization — decompose into prime building blocks
• Find GCF of 77280 and another number
• Find LCM of 77280 and another number
• Is 77280 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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