Divisors of 58320: All 70 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 58320

The number 58320 has 70 divisors:

1,  2,  3,  4,  5,  6,  8,  9,  10,  12,  15,  16,  18,  20,  24,  27,  30,  36,  40,  45,  48,  54,  60,  72,  80,  81,  90,  108,  120,  135,  144,  162,  180,  216,  240,  243,  270,  324,  360,  405,  432,  486,  540,  648,  720,  729,  810,  972,  1080,  1215,  1296,  1458,  1620,  1944,  2160,  2430,  2916,  3240,  3645,  3888,  4860,  5832,  6480,  7290,  9720,  11664,  14580,  19440,  29160,  58320

Divisor Pairs of 58320

Each pair multiplies to 58320:

Number of Divisors

The number 58320 has 70 divisors, written as τ(58320) = 70 in number theory.

Sum of Divisors

σ(58320) = 1 + 2 + 3 + 4 + 5 + 6 + 8 + 9 + 10 + 12 + 15 + 16 + 18 + 20 + 24 + 27 + 30 + 36 + 40 + 45 + 48 + 54 + 60 + 72 + 80 + 81 + 90 + 108 + 120 + 135 + 144 + 162 + 180 + 216 + 240 + 243 + 270 + 324 + 360 + 405 + 432 + 486 + 540 + 648 + 720 + 729 + 810 + 972 + 1080 + 1215 + 1296 + 1458 + 1620 + 1944 + 2160 + 2430 + 2916 + 3240 + 3645 + 3888 + 4860 + 5832 + 6480 + 7290 + 9720 + 11664 + 14580 + 19440 + 29160 + 58320 = 203298

Prime Factorization of 58320

See the full prime factorization calculator →

Properties of 58320

• 58320 is composite.
• 58320 is not a perfect square.
• Number of divisors: 70.
• Sum of divisors: 203298.

Common Divisors with Another Number?

Looking for the divisors that 58320 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 58320

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √58320 ≈ 241.50. If i divides 58320, then both i and 58320/i are divisors.

1. 1 divides 58320 (58320 ÷ 1 = 58320) → pair (1, 58320)
2. 2 divides 58320 (58320 ÷ 2 = 29160) → pair (2, 29160)
3. 3 divides 58320 (58320 ÷ 3 = 19440) → pair (3, 19440)
4. 4 divides 58320 (58320 ÷ 4 = 14580) → pair (4, 14580)
5. 5 divides 58320 (58320 ÷ 5 = 11664) → pair (5, 11664)
6. 6 divides 58320 (58320 ÷ 6 = 9720) → pair (6, 9720)
7. 8 divides 58320 (58320 ÷ 8 = 7290) → pair (8, 7290)
8. 9 divides 58320 (58320 ÷ 9 = 6480) → pair (9, 6480)
9. 10 divides 58320 (58320 ÷ 10 = 5832) → pair (10, 5832)
10. 12 divides 58320 (58320 ÷ 12 = 4860) → pair (12, 4860)
11. 15 divides 58320 (58320 ÷ 15 = 3888) → pair (15, 3888)
12. 16 divides 58320 (58320 ÷ 16 = 3645) → pair (16, 3645)
13. 18 divides 58320 (58320 ÷ 18 = 3240) → pair (18, 3240)
14. 20 divides 58320 (58320 ÷ 20 = 2916) → pair (20, 2916)
15. 24 divides 58320 (58320 ÷ 24 = 2430) → pair (24, 2430)
16. 27 divides 58320 (58320 ÷ 27 = 2160) → pair (27, 2160)
17. 30 divides 58320 (58320 ÷ 30 = 1944) → pair (30, 1944)
18. 36 divides 58320 (58320 ÷ 36 = 1620) → pair (36, 1620)
19. 40 divides 58320 (58320 ÷ 40 = 1458) → pair (40, 1458)
20. 45 divides 58320 (58320 ÷ 45 = 1296) → pair (45, 1296)
21. 48 divides 58320 (58320 ÷ 48 = 1215) → pair (48, 1215)
22. 54 divides 58320 (58320 ÷ 54 = 1080) → pair (54, 1080)
23. 60 divides 58320 (58320 ÷ 60 = 972) → pair (60, 972)
24. 72 divides 58320 (58320 ÷ 72 = 810) → pair (72, 810)
25. 80 divides 58320 (58320 ÷ 80 = 729) → pair (80, 729)
26. 81 divides 58320 (58320 ÷ 81 = 720) → pair (81, 720)
27. 90 divides 58320 (58320 ÷ 90 = 648) → pair (90, 648)
28. 108 divides 58320 (58320 ÷ 108 = 540) → pair (108, 540)
29. 120 divides 58320 (58320 ÷ 120 = 486) → pair (120, 486)
30. 135 divides 58320 (58320 ÷ 135 = 432) → pair (135, 432)
31. 144 divides 58320 (58320 ÷ 144 = 405) → pair (144, 405)
32. 162 divides 58320 (58320 ÷ 162 = 360) → pair (162, 360)
33. 180 divides 58320 (58320 ÷ 180 = 324) → pair (180, 324)
34. 216 divides 58320 (58320 ÷ 216 = 270) → pair (216, 270)
35. 240 divides 58320 (58320 ÷ 240 = 243) → pair (240, 243)
36. Collect all unique values: {1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 27, 30, 36, 40, 45, 48, 54, 60, 72, 80, 81, 90, 108, 120, 135, 144, 162, 180, 216, 240, 243, 270, 324, 360, 405, 432, 486, 540, 648, 720, 729, 810, 972, 1080, 1215, 1296, 1458, 1620, 1944, 2160, 2430, 2916, 3240, 3645, 3888, 4860, 5832, 6480, 7290, 9720, 11664, 14580, 19440, 29160, 58320} — total 70 divisors.
37. Sum: 1 + 2 + 3 + 4 + 5 + 6 + 8 + 9 + 10 + 12 + 15 + 16 + 18 + 20 + 24 + 27 + 30 + 36 + 40 + 45 + 48 + 54 + 60 + 72 + 80 + 81 + 90 + 108 + 120 + 135 + 144 + 162 + 180 + 216 + 240 + 243 + 270 + 324 + 360 + 405 + 432 + 486 + 540 + 648 + 720 + 729 + 810 + 972 + 1080 + 1215 + 1296 + 1458 + 1620 + 1944 + 2160 + 2430 + 2916 + 3240 + 3645 + 3888 + 4860 + 5832 + 6480 + 7290 + 9720 + 11664 + 14580 + 19440 + 29160 + 58320 = 203298.

Nearby Examples

Related Operations for 58320

• Multiples of a Number — "outward" complement of divisors
• 58320 Prime Factorization — decompose into prime building blocks
• Find GCF of 58320 and another number
• Find LCM of 58320 and another number
• Is 58320 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)

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