Divisors of 72960: 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 72960

The number 72960 has 72 divisors:

1,  2,  3,  4,  5,  6,  8,  10,  12,  15,  16,  19,  20,  24,  30,  32,  38,  40,  48,  57,  60,  64,  76,  80,  95,  96,  114,  120,  128,  152,  160,  190,  192,  228,  240,  256,  285,  304,  320,  380,  384,  456,  480,  570,  608,  640,  760,  768,  912,  960,  1140,  1216,  1280,  1520,  1824,  1920,  2280,  2432,  3040,  3648,  3840,  4560,  4864,  6080,  7296,  9120,  12160,  14592,  18240,  24320,  36480,  72960

Divisor Pairs of 72960

Each pair multiplies to 72960:

Number of Divisors

The number 72960 has 72 divisors, written as τ(72960) = 72 in number theory.

Sum of Divisors

σ(72960) = 1 + 2 + 3 + 4 + 5 + 6 + 8 + 10 + 12 + 15 + 16 + 19 + 20 + 24 + 30 + 32 + 38 + 40 + 48 + 57 + 60 + 64 + 76 + 80 + 95 + 96 + 114 + 120 + 128 + 152 + 160 + 190 + 192 + 228 + 240 + 256 + 285 + 304 + 320 + 380 + 384 + 456 + 480 + 570 + 608 + 640 + 760 + 768 + 912 + 960 + 1140 + 1216 + 1280 + 1520 + 1824 + 1920 + 2280 + 2432 + 3040 + 3648 + 3840 + 4560 + 4864 + 6080 + 7296 + 9120 + 12160 + 14592 + 18240 + 24320 + 36480 + 72960 = 245280

Prime Factorization of 72960

See the full prime factorization calculator →

Properties of 72960

• 72960 is composite.
• 72960 is not a perfect square.
• Number of divisors: 72.
• Sum of divisors: 245280.

Common Divisors with Another Number?

Looking for the divisors that 72960 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 72960

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √72960 ≈ 270.11. If i divides 72960, then both i and 72960/i are divisors.

1. 1 divides 72960 (72960 ÷ 1 = 72960) → pair (1, 72960)
2. 2 divides 72960 (72960 ÷ 2 = 36480) → pair (2, 36480)
3. 3 divides 72960 (72960 ÷ 3 = 24320) → pair (3, 24320)
4. 4 divides 72960 (72960 ÷ 4 = 18240) → pair (4, 18240)
5. 5 divides 72960 (72960 ÷ 5 = 14592) → pair (5, 14592)
6. 6 divides 72960 (72960 ÷ 6 = 12160) → pair (6, 12160)
7. 8 divides 72960 (72960 ÷ 8 = 9120) → pair (8, 9120)
8. 10 divides 72960 (72960 ÷ 10 = 7296) → pair (10, 7296)
9. 12 divides 72960 (72960 ÷ 12 = 6080) → pair (12, 6080)
10. 15 divides 72960 (72960 ÷ 15 = 4864) → pair (15, 4864)
11. 16 divides 72960 (72960 ÷ 16 = 4560) → pair (16, 4560)
12. 19 divides 72960 (72960 ÷ 19 = 3840) → pair (19, 3840)
13. 20 divides 72960 (72960 ÷ 20 = 3648) → pair (20, 3648)
14. 24 divides 72960 (72960 ÷ 24 = 3040) → pair (24, 3040)
15. 30 divides 72960 (72960 ÷ 30 = 2432) → pair (30, 2432)
16. 32 divides 72960 (72960 ÷ 32 = 2280) → pair (32, 2280)
17. 38 divides 72960 (72960 ÷ 38 = 1920) → pair (38, 1920)
18. 40 divides 72960 (72960 ÷ 40 = 1824) → pair (40, 1824)
19. 48 divides 72960 (72960 ÷ 48 = 1520) → pair (48, 1520)
20. 57 divides 72960 (72960 ÷ 57 = 1280) → pair (57, 1280)
21. 60 divides 72960 (72960 ÷ 60 = 1216) → pair (60, 1216)
22. 64 divides 72960 (72960 ÷ 64 = 1140) → pair (64, 1140)
23. 76 divides 72960 (72960 ÷ 76 = 960) → pair (76, 960)
24. 80 divides 72960 (72960 ÷ 80 = 912) → pair (80, 912)
25. 95 divides 72960 (72960 ÷ 95 = 768) → pair (95, 768)
26. 96 divides 72960 (72960 ÷ 96 = 760) → pair (96, 760)
27. 114 divides 72960 (72960 ÷ 114 = 640) → pair (114, 640)
28. 120 divides 72960 (72960 ÷ 120 = 608) → pair (120, 608)
29. 128 divides 72960 (72960 ÷ 128 = 570) → pair (128, 570)
30. 152 divides 72960 (72960 ÷ 152 = 480) → pair (152, 480)
31. 160 divides 72960 (72960 ÷ 160 = 456) → pair (160, 456)
32. 190 divides 72960 (72960 ÷ 190 = 384) → pair (190, 384)
33. 192 divides 72960 (72960 ÷ 192 = 380) → pair (192, 380)
34. 228 divides 72960 (72960 ÷ 228 = 320) → pair (228, 320)
35. 240 divides 72960 (72960 ÷ 240 = 304) → pair (240, 304)
36. 256 divides 72960 (72960 ÷ 256 = 285) → pair (256, 285)
37. Collect all unique values: {1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 19, 20, 24, 30, 32, 38, 40, 48, 57, 60, 64, 76, 80, 95, 96, 114, 120, 128, 152, 160, 190, 192, 228, 240, 256, 285, 304, 320, 380, 384, 456, 480, 570, 608, 640, 760, 768, 912, 960, 1140, 1216, 1280, 1520, 1824, 1920, 2280, 2432, 3040, 3648, 3840, 4560, 4864, 6080, 7296, 9120, 12160, 14592, 18240, 24320, 36480, 72960} — total 72 divisors.
38. Sum: 1 + 2 + 3 + 4 + 5 + 6 + 8 + 10 + 12 + 15 + 16 + 19 + 20 + 24 + 30 + 32 + 38 + 40 + 48 + 57 + 60 + 64 + 76 + 80 + 95 + 96 + 114 + 120 + 128 + 152 + 160 + 190 + 192 + 228 + 240 + 256 + 285 + 304 + 320 + 380 + 384 + 456 + 480 + 570 + 608 + 640 + 760 + 768 + 912 + 960 + 1140 + 1216 + 1280 + 1520 + 1824 + 1920 + 2280 + 2432 + 3040 + 3648 + 3840 + 4560 + 4864 + 6080 + 7296 + 9120 + 12160 + 14592 + 18240 + 24320 + 36480 + 72960 = 245280.

Nearby Examples

Related Operations for 72960

• Multiples of a Number — "outward" complement of divisors
• 72960 Prime Factorization — decompose into prime building blocks
• Find GCF of 72960 and another number
• Find LCM of 72960 and another number
• Is 72960 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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