Divisors of 77760: All 84 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 77760

The number 77760 has 84 divisors:

1,  2,  3,  4,  5,  6,  8,  9,  10,  12,  15,  16,  18,  20,  24,  27,  30,  32,  36,  40,  45,  48,  54,  60,  64,  72,  80,  81,  90,  96,  108,  120,  135,  144,  160,  162,  180,  192,  216,  240,  243,  270,  288,  320,  324,  360,  405,  432,  480,  486,  540,  576,  648,  720,  810,  864,  960,  972,  1080,  1215,  1296,  1440,  1620,  1728,  1944,  2160,  2430,  2592,  2880,  3240,  3888,  4320,  4860,  5184,  6480,  7776,  8640,  9720,  12960,  15552,  19440,  25920,  38880,  77760

Divisor Pairs of 77760

Each pair multiplies to 77760:

Number of Divisors

The number 77760 has 84 divisors, written as τ(77760) = 84 in number theory.

Sum of Divisors

σ(77760) = 1 + 2 + 3 + 4 + 5 + 6 + 8 + 9 + 10 + 12 + 15 + 16 + 18 + 20 + 24 + 27 + 30 + 32 + 36 + 40 + 45 + 48 + 54 + 60 + 64 + 72 + 80 + 81 + 90 + 96 + 108 + 120 + 135 + 144 + 160 + 162 + 180 + 192 + 216 + 240 + 243 + 270 + 288 + 320 + 324 + 360 + 405 + 432 + 480 + 486 + 540 + 576 + 648 + 720 + 810 + 864 + 960 + 972 + 1080 + 1215 + 1296 + 1440 + 1620 + 1728 + 1944 + 2160 + 2430 + 2592 + 2880 + 3240 + 3888 + 4320 + 4860 + 5184 + 6480 + 7776 + 8640 + 9720 + 12960 + 15552 + 19440 + 25920 + 38880 + 77760 = 277368

Prime Factorization of 77760

See the full prime factorization calculator →

Properties of 77760

• 77760 is composite.
• 77760 is not a perfect square.
• Number of divisors: 84.
• Sum of divisors: 277368.

Common Divisors with Another Number?

Looking for the divisors that 77760 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 77760

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √77760 ≈ 278.85. If i divides 77760, then both i and 77760/i are divisors.

1. 1 divides 77760 (77760 ÷ 1 = 77760) → pair (1, 77760)
2. 2 divides 77760 (77760 ÷ 2 = 38880) → pair (2, 38880)
3. 3 divides 77760 (77760 ÷ 3 = 25920) → pair (3, 25920)
4. 4 divides 77760 (77760 ÷ 4 = 19440) → pair (4, 19440)
5. 5 divides 77760 (77760 ÷ 5 = 15552) → pair (5, 15552)
6. 6 divides 77760 (77760 ÷ 6 = 12960) → pair (6, 12960)
7. 8 divides 77760 (77760 ÷ 8 = 9720) → pair (8, 9720)
8. 9 divides 77760 (77760 ÷ 9 = 8640) → pair (9, 8640)
9. 10 divides 77760 (77760 ÷ 10 = 7776) → pair (10, 7776)
10. 12 divides 77760 (77760 ÷ 12 = 6480) → pair (12, 6480)
11. 15 divides 77760 (77760 ÷ 15 = 5184) → pair (15, 5184)
12. 16 divides 77760 (77760 ÷ 16 = 4860) → pair (16, 4860)
13. 18 divides 77760 (77760 ÷ 18 = 4320) → pair (18, 4320)
14. 20 divides 77760 (77760 ÷ 20 = 3888) → pair (20, 3888)
15. 24 divides 77760 (77760 ÷ 24 = 3240) → pair (24, 3240)
16. 27 divides 77760 (77760 ÷ 27 = 2880) → pair (27, 2880)
17. 30 divides 77760 (77760 ÷ 30 = 2592) → pair (30, 2592)
18. 32 divides 77760 (77760 ÷ 32 = 2430) → pair (32, 2430)
19. 36 divides 77760 (77760 ÷ 36 = 2160) → pair (36, 2160)
20. 40 divides 77760 (77760 ÷ 40 = 1944) → pair (40, 1944)
21. 45 divides 77760 (77760 ÷ 45 = 1728) → pair (45, 1728)
22. 48 divides 77760 (77760 ÷ 48 = 1620) → pair (48, 1620)
23. 54 divides 77760 (77760 ÷ 54 = 1440) → pair (54, 1440)
24. 60 divides 77760 (77760 ÷ 60 = 1296) → pair (60, 1296)
25. 64 divides 77760 (77760 ÷ 64 = 1215) → pair (64, 1215)
26. 72 divides 77760 (77760 ÷ 72 = 1080) → pair (72, 1080)
27. 80 divides 77760 (77760 ÷ 80 = 972) → pair (80, 972)
28. 81 divides 77760 (77760 ÷ 81 = 960) → pair (81, 960)
29. 90 divides 77760 (77760 ÷ 90 = 864) → pair (90, 864)
30. 96 divides 77760 (77760 ÷ 96 = 810) → pair (96, 810)
31. 108 divides 77760 (77760 ÷ 108 = 720) → pair (108, 720)
32. 120 divides 77760 (77760 ÷ 120 = 648) → pair (120, 648)
33. 135 divides 77760 (77760 ÷ 135 = 576) → pair (135, 576)
34. 144 divides 77760 (77760 ÷ 144 = 540) → pair (144, 540)
35. 160 divides 77760 (77760 ÷ 160 = 486) → pair (160, 486)
36. 162 divides 77760 (77760 ÷ 162 = 480) → pair (162, 480)
37. 180 divides 77760 (77760 ÷ 180 = 432) → pair (180, 432)
38. 192 divides 77760 (77760 ÷ 192 = 405) → pair (192, 405)
39. 216 divides 77760 (77760 ÷ 216 = 360) → pair (216, 360)
40. 240 divides 77760 (77760 ÷ 240 = 324) → pair (240, 324)
41. 243 divides 77760 (77760 ÷ 243 = 320) → pair (243, 320)
42. 270 divides 77760 (77760 ÷ 270 = 288) → pair (270, 288)
43. Collect all unique values: {1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 27, 30, 32, 36, 40, 45, 48, 54, 60, 64, 72, 80, 81, 90, 96, 108, 120, 135, 144, 160, 162, 180, 192, 216, 240, 243, 270, 288, 320, 324, 360, 405, 432, 480, 486, 540, 576, 648, 720, 810, 864, 960, 972, 1080, 1215, 1296, 1440, 1620, 1728, 1944, 2160, 2430, 2592, 2880, 3240, 3888, 4320, 4860, 5184, 6480, 7776, 8640, 9720, 12960, 15552, 19440, 25920, 38880, 77760} — total 84 divisors.
44. Sum: 1 + 2 + 3 + 4 + 5 + 6 + 8 + 9 + 10 + 12 + 15 + 16 + 18 + 20 + 24 + 27 + 30 + 32 + 36 + 40 + 45 + 48 + 54 + 60 + 64 + 72 + 80 + 81 + 90 + 96 + 108 + 120 + 135 + 144 + 160 + 162 + 180 + 192 + 216 + 240 + 243 + 270 + 288 + 320 + 324 + 360 + 405 + 432 + 480 + 486 + 540 + 576 + 648 + 720 + 810 + 864 + 960 + 972 + 1080 + 1215 + 1296 + 1440 + 1620 + 1728 + 1944 + 2160 + 2430 + 2592 + 2880 + 3240 + 3888 + 4320 + 4860 + 5184 + 6480 + 7776 + 8640 + 9720 + 12960 + 15552 + 19440 + 25920 + 38880 + 77760 = 277368.

Nearby Examples

Related Operations for 77760

• Multiples of a Number — "outward" complement of divisors
• 77760 Prime Factorization — decompose into prime building blocks
• Find GCF of 77760 and another number
• Find LCM of 77760 and another number
• Is 77760 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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