Divisors of 58080: All 72 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 58080

The number 58080 has 72 divisors:

1,  2,  3,  4,  5,  6,  8,  10,  11,  12,  15,  16,  20,  22,  24,  30,  32,  33,  40,  44,  48,  55,  60,  66,  80,  88,  96,  110,  120,  121,  132,  160,  165,  176,  220,  240,  242,  264,  330,  352,  363,  440,  480,  484,  528,  605,  660,  726,  880,  968,  1056,  1210,  1320,  1452,  1760,  1815,  1936,  2420,  2640,  2904,  3630,  3872,  4840,  5280,  5808,  7260,  9680,  11616,  14520,  19360,  29040,  58080

Divisor Pairs of 58080

Each pair multiplies to 58080:

Number of Divisors

The number 58080 has 72 divisors, written as τ(58080) = 72 in number theory.

Sum of Divisors

σ(58080) = 1 + 2 + 3 + 4 + 5 + 6 + 8 + 10 + 11 + 12 + 15 + 16 + 20 + 22 + 24 + 30 + 32 + 33 + 40 + 44 + 48 + 55 + 60 + 66 + 80 + 88 + 96 + 110 + 120 + 121 + 132 + 160 + 165 + 176 + 220 + 240 + 242 + 264 + 330 + 352 + 363 + 440 + 480 + 484 + 528 + 605 + 660 + 726 + 880 + 968 + 1056 + 1210 + 1320 + 1452 + 1760 + 1815 + 1936 + 2420 + 2640 + 2904 + 3630 + 3872 + 4840 + 5280 + 5808 + 7260 + 9680 + 11616 + 14520 + 19360 + 29040 + 58080 = 201096

Prime Factorization of 58080

See the full prime factorization calculator →

Properties of 58080

• 58080 is composite.
• 58080 is not a perfect square.
• Number of divisors: 72.
• Sum of divisors: 201096.

Common Divisors with Another Number?

Looking for the divisors that 58080 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 58080

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √58080 ≈ 241.00. If i divides 58080, then both i and 58080/i are divisors.

1. 1 divides 58080 (58080 ÷ 1 = 58080) → pair (1, 58080)
2. 2 divides 58080 (58080 ÷ 2 = 29040) → pair (2, 29040)
3. 3 divides 58080 (58080 ÷ 3 = 19360) → pair (3, 19360)
4. 4 divides 58080 (58080 ÷ 4 = 14520) → pair (4, 14520)
5. 5 divides 58080 (58080 ÷ 5 = 11616) → pair (5, 11616)
6. 6 divides 58080 (58080 ÷ 6 = 9680) → pair (6, 9680)
7. 8 divides 58080 (58080 ÷ 8 = 7260) → pair (8, 7260)
8. 10 divides 58080 (58080 ÷ 10 = 5808) → pair (10, 5808)
9. 11 divides 58080 (58080 ÷ 11 = 5280) → pair (11, 5280)
10. 12 divides 58080 (58080 ÷ 12 = 4840) → pair (12, 4840)
11. 15 divides 58080 (58080 ÷ 15 = 3872) → pair (15, 3872)
12. 16 divides 58080 (58080 ÷ 16 = 3630) → pair (16, 3630)
13. 20 divides 58080 (58080 ÷ 20 = 2904) → pair (20, 2904)
14. 22 divides 58080 (58080 ÷ 22 = 2640) → pair (22, 2640)
15. 24 divides 58080 (58080 ÷ 24 = 2420) → pair (24, 2420)
16. 30 divides 58080 (58080 ÷ 30 = 1936) → pair (30, 1936)
17. 32 divides 58080 (58080 ÷ 32 = 1815) → pair (32, 1815)
18. 33 divides 58080 (58080 ÷ 33 = 1760) → pair (33, 1760)
19. 40 divides 58080 (58080 ÷ 40 = 1452) → pair (40, 1452)
20. 44 divides 58080 (58080 ÷ 44 = 1320) → pair (44, 1320)
21. 48 divides 58080 (58080 ÷ 48 = 1210) → pair (48, 1210)
22. 55 divides 58080 (58080 ÷ 55 = 1056) → pair (55, 1056)
23. 60 divides 58080 (58080 ÷ 60 = 968) → pair (60, 968)
24. 66 divides 58080 (58080 ÷ 66 = 880) → pair (66, 880)
25. 80 divides 58080 (58080 ÷ 80 = 726) → pair (80, 726)
26. 88 divides 58080 (58080 ÷ 88 = 660) → pair (88, 660)
27. 96 divides 58080 (58080 ÷ 96 = 605) → pair (96, 605)
28. 110 divides 58080 (58080 ÷ 110 = 528) → pair (110, 528)
29. 120 divides 58080 (58080 ÷ 120 = 484) → pair (120, 484)
30. 121 divides 58080 (58080 ÷ 121 = 480) → pair (121, 480)
31. 132 divides 58080 (58080 ÷ 132 = 440) → pair (132, 440)
32. 160 divides 58080 (58080 ÷ 160 = 363) → pair (160, 363)
33. 165 divides 58080 (58080 ÷ 165 = 352) → pair (165, 352)
34. 176 divides 58080 (58080 ÷ 176 = 330) → pair (176, 330)
35. 220 divides 58080 (58080 ÷ 220 = 264) → pair (220, 264)
36. 240 divides 58080 (58080 ÷ 240 = 242) → pair (240, 242)
37. Collect all unique values: {1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 16, 20, 22, 24, 30, 32, 33, 40, 44, 48, 55, 60, 66, 80, 88, 96, 110, 120, 121, 132, 160, 165, 176, 220, 240, 242, 264, 330, 352, 363, 440, 480, 484, 528, 605, 660, 726, 880, 968, 1056, 1210, 1320, 1452, 1760, 1815, 1936, 2420, 2640, 2904, 3630, 3872, 4840, 5280, 5808, 7260, 9680, 11616, 14520, 19360, 29040, 58080} — total 72 divisors.
38. Sum: 1 + 2 + 3 + 4 + 5 + 6 + 8 + 10 + 11 + 12 + 15 + 16 + 20 + 22 + 24 + 30 + 32 + 33 + 40 + 44 + 48 + 55 + 60 + 66 + 80 + 88 + 96 + 110 + 120 + 121 + 132 + 160 + 165 + 176 + 220 + 240 + 242 + 264 + 330 + 352 + 363 + 440 + 480 + 484 + 528 + 605 + 660 + 726 + 880 + 968 + 1056 + 1210 + 1320 + 1452 + 1760 + 1815 + 1936 + 2420 + 2640 + 2904 + 3630 + 3872 + 4840 + 5280 + 5808 + 7260 + 9680 + 11616 + 14520 + 19360 + 29040 + 58080 = 201096.

Nearby Examples

Related Operations for 58080

• Multiples of a Number — "outward" complement of divisors
• 58080 Prime Factorization — decompose into prime building blocks
• Find GCF of 58080 and another number
• Find LCM of 58080 and another number
• Is 58080 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: