Divisors of 59040: 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 59040

The number 59040 has 72 divisors:

1,  2,  3,  4,  5,  6,  8,  9,  10,  12,  15,  16,  18,  20,  24,  30,  32,  36,  40,  41,  45,  48,  60,  72,  80,  82,  90,  96,  120,  123,  144,  160,  164,  180,  205,  240,  246,  288,  328,  360,  369,  410,  480,  492,  615,  656,  720,  738,  820,  984,  1230,  1312,  1440,  1476,  1640,  1845,  1968,  2460,  2952,  3280,  3690,  3936,  4920,  5904,  6560,  7380,  9840,  11808,  14760,  19680,  29520,  59040

Divisor Pairs of 59040

Each pair multiplies to 59040:

Number of Divisors

The number 59040 has 72 divisors, written as τ(59040) = 72 in number theory.

Sum of Divisors

σ(59040) = 1 + 2 + 3 + 4 + 5 + 6 + 8 + 9 + 10 + 12 + 15 + 16 + 18 + 20 + 24 + 30 + 32 + 36 + 40 + 41 + 45 + 48 + 60 + 72 + 80 + 82 + 90 + 96 + 120 + 123 + 144 + 160 + 164 + 180 + 205 + 240 + 246 + 288 + 328 + 360 + 369 + 410 + 480 + 492 + 615 + 656 + 720 + 738 + 820 + 984 + 1230 + 1312 + 1440 + 1476 + 1640 + 1845 + 1968 + 2460 + 2952 + 3280 + 3690 + 3936 + 4920 + 5904 + 6560 + 7380 + 9840 + 11808 + 14760 + 19680 + 29520 + 59040 = 206388

Prime Factorization of 59040

See the full prime factorization calculator →

Properties of 59040

• 59040 is composite.
• 59040 is not a perfect square.
• Number of divisors: 72.
• Sum of divisors: 206388.

Common Divisors with Another Number?

Looking for the divisors that 59040 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 59040

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √59040 ≈ 242.98. If i divides 59040, then both i and 59040/i are divisors.

1. 1 divides 59040 (59040 ÷ 1 = 59040) → pair (1, 59040)
2. 2 divides 59040 (59040 ÷ 2 = 29520) → pair (2, 29520)
3. 3 divides 59040 (59040 ÷ 3 = 19680) → pair (3, 19680)
4. 4 divides 59040 (59040 ÷ 4 = 14760) → pair (4, 14760)
5. 5 divides 59040 (59040 ÷ 5 = 11808) → pair (5, 11808)
6. 6 divides 59040 (59040 ÷ 6 = 9840) → pair (6, 9840)
7. 8 divides 59040 (59040 ÷ 8 = 7380) → pair (8, 7380)
8. 9 divides 59040 (59040 ÷ 9 = 6560) → pair (9, 6560)
9. 10 divides 59040 (59040 ÷ 10 = 5904) → pair (10, 5904)
10. 12 divides 59040 (59040 ÷ 12 = 4920) → pair (12, 4920)
11. 15 divides 59040 (59040 ÷ 15 = 3936) → pair (15, 3936)
12. 16 divides 59040 (59040 ÷ 16 = 3690) → pair (16, 3690)
13. 18 divides 59040 (59040 ÷ 18 = 3280) → pair (18, 3280)
14. 20 divides 59040 (59040 ÷ 20 = 2952) → pair (20, 2952)
15. 24 divides 59040 (59040 ÷ 24 = 2460) → pair (24, 2460)
16. 30 divides 59040 (59040 ÷ 30 = 1968) → pair (30, 1968)
17. 32 divides 59040 (59040 ÷ 32 = 1845) → pair (32, 1845)
18. 36 divides 59040 (59040 ÷ 36 = 1640) → pair (36, 1640)
19. 40 divides 59040 (59040 ÷ 40 = 1476) → pair (40, 1476)
20. 41 divides 59040 (59040 ÷ 41 = 1440) → pair (41, 1440)
21. 45 divides 59040 (59040 ÷ 45 = 1312) → pair (45, 1312)
22. 48 divides 59040 (59040 ÷ 48 = 1230) → pair (48, 1230)
23. 60 divides 59040 (59040 ÷ 60 = 984) → pair (60, 984)
24. 72 divides 59040 (59040 ÷ 72 = 820) → pair (72, 820)
25. 80 divides 59040 (59040 ÷ 80 = 738) → pair (80, 738)
26. 82 divides 59040 (59040 ÷ 82 = 720) → pair (82, 720)
27. 90 divides 59040 (59040 ÷ 90 = 656) → pair (90, 656)
28. 96 divides 59040 (59040 ÷ 96 = 615) → pair (96, 615)
29. 120 divides 59040 (59040 ÷ 120 = 492) → pair (120, 492)
30. 123 divides 59040 (59040 ÷ 123 = 480) → pair (123, 480)
31. 144 divides 59040 (59040 ÷ 144 = 410) → pair (144, 410)
32. 160 divides 59040 (59040 ÷ 160 = 369) → pair (160, 369)
33. 164 divides 59040 (59040 ÷ 164 = 360) → pair (164, 360)
34. 180 divides 59040 (59040 ÷ 180 = 328) → pair (180, 328)
35. 205 divides 59040 (59040 ÷ 205 = 288) → pair (205, 288)
36. 240 divides 59040 (59040 ÷ 240 = 246) → pair (240, 246)
37. Collect all unique values: {1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 32, 36, 40, 41, 45, 48, 60, 72, 80, 82, 90, 96, 120, 123, 144, 160, 164, 180, 205, 240, 246, 288, 328, 360, 369, 410, 480, 492, 615, 656, 720, 738, 820, 984, 1230, 1312, 1440, 1476, 1640, 1845, 1968, 2460, 2952, 3280, 3690, 3936, 4920, 5904, 6560, 7380, 9840, 11808, 14760, 19680, 29520, 59040} — total 72 divisors.
38. Sum: 1 + 2 + 3 + 4 + 5 + 6 + 8 + 9 + 10 + 12 + 15 + 16 + 18 + 20 + 24 + 30 + 32 + 36 + 40 + 41 + 45 + 48 + 60 + 72 + 80 + 82 + 90 + 96 + 120 + 123 + 144 + 160 + 164 + 180 + 205 + 240 + 246 + 288 + 328 + 360 + 369 + 410 + 480 + 492 + 615 + 656 + 720 + 738 + 820 + 984 + 1230 + 1312 + 1440 + 1476 + 1640 + 1845 + 1968 + 2460 + 2952 + 3280 + 3690 + 3936 + 4920 + 5904 + 6560 + 7380 + 9840 + 11808 + 14760 + 19680 + 29520 + 59040 = 206388.

Nearby Examples

Related Operations for 59040

• Multiples of a Number — "outward" complement of divisors
• 59040 Prime Factorization — decompose into prime building blocks
• Find GCF of 59040 and another number
• Find LCM of 59040 and another number
• Is 59040 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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