Divisors of 76320: All 72 Factors

Quick Answer

76320 has 72 divisors (factors): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 32, 36, 40, 45, 48, 53, 60, 72, 80, 90, 96, 106, 120, 144, 159, 160, 180, 212, 240, 265, 288, 318, 360, 424, 477, 480, 530, 636, 720, 795, 848, 954, 1060, 1272, 1440, 1590, 1696, 1908, 2120, 2385, 2544, 3180, 3816, 4240, 4770, 5088, 6360, 7632, 8480, 9540, 12720, 15264, 19080, 25440, 38160, 76320.

Sum: 265356.

Divisors (Factors) Calculator

Divisors Multiples Prime Factoriz. GCF LCM

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72 divisors
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 32, 36, 40, 45, 48, 53, 60, 72, 80, 90, 96, 106, 120, 144, 159, 160, 180, 212, 240, 265, 288, 318, 360, 424, 477, 480, 530, 636, 720, 795, 848, 954, 1060, 1272, 1440, 1590, 1696, 1908, 2120, 2385, 2544, 3180, 3816, 4240, 4770, 5088, 6360, 7632, 8480, 9540, 12720, 15264, 19080, 25440, 38160, 76320

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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 76320

The number 76320 has 72 divisors:

1,  2,  3,  4,  5,  6,  8,  9,  10,  12,  15,  16,  18,  20,  24,  30,  32,  36,  40,  45,  48,  53,  60,  72,  80,  90,  96,  106,  120,  144,  159,  160,  180,  212,  240,  265,  288,  318,  360,  424,  477,  480,  530,  636,  720,  795,  848,  954,  1060,  1272,  1440,  1590,  1696,  1908,  2120,  2385,  2544,  3180,  3816,  4240,  4770,  5088,  6360,  7632,  8480,  9540,  12720,  15264,  19080,  25440,  38160,  76320

Divisor Pairs of 76320

Each pair multiplies to 76320:

Factor 1×Factor 2=Product
1×76320=76320
2×38160=76320
3×25440=76320
4×19080=76320
5×15264=76320
6×12720=76320
8×9540=76320
9×8480=76320
10×7632=76320
12×6360=76320
15×5088=76320
16×4770=76320
18×4240=76320
20×3816=76320
24×3180=76320
30×2544=76320
32×2385=76320
36×2120=76320
40×1908=76320
45×1696=76320
48×1590=76320
53×1440=76320
60×1272=76320
72×1060=76320
80×954=76320
90×848=76320
96×795=76320
106×720=76320
120×636=76320
144×530=76320
159×480=76320
160×477=76320
180×424=76320
212×360=76320
240×318=76320
265×288=76320

Number of Divisors

The number 76320 has 72 divisors, written as τ(76320) = 72 in number theory.

Sum of Divisors

σ(76320) = 1 + 2 + 3 + 4 + 5 + 6 + 8 + 9 + 10 + 12 + 15 + 16 + 18 + 20 + 24 + 30 + 32 + 36 + 40 + 45 + 48 + 53 + 60 + 72 + 80 + 90 + 96 + 106 + 120 + 144 + 159 + 160 + 180 + 212 + 240 + 265 + 288 + 318 + 360 + 424 + 477 + 480 + 530 + 636 + 720 + 795 + 848 + 954 + 1060 + 1272 + 1440 + 1590 + 1696 + 1908 + 2120 + 2385 + 2544 + 3180 + 3816 + 4240 + 4770 + 5088 + 6360 + 7632 + 8480 + 9540 + 12720 + 15264 + 19080 + 25440 + 38160 + 76320 = 265356

Prime Factorization of 76320

See the full prime factorization calculator →

Properties of 76320

  • 76320 is composite.
  • 76320 is not a perfect square.
  • Number of divisors: 72.
  • Sum of divisors: 265356.

Common Divisors with Another Number?

Looking for the divisors that 76320 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 76320

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √76320 ≈ 276.26. If i divides 76320, then both i and 76320/i are divisors.

  1. 1 divides 76320 (76320 ÷ 1 = 76320) → pair (1, 76320)
  2. 2 divides 76320 (76320 ÷ 2 = 38160) → pair (2, 38160)
  3. 3 divides 76320 (76320 ÷ 3 = 25440) → pair (3, 25440)
  4. 4 divides 76320 (76320 ÷ 4 = 19080) → pair (4, 19080)
  5. 5 divides 76320 (76320 ÷ 5 = 15264) → pair (5, 15264)
  6. 6 divides 76320 (76320 ÷ 6 = 12720) → pair (6, 12720)
  7. 8 divides 76320 (76320 ÷ 8 = 9540) → pair (8, 9540)
  8. 9 divides 76320 (76320 ÷ 9 = 8480) → pair (9, 8480)
  9. 10 divides 76320 (76320 ÷ 10 = 7632) → pair (10, 7632)
  10. 12 divides 76320 (76320 ÷ 12 = 6360) → pair (12, 6360)
  11. 15 divides 76320 (76320 ÷ 15 = 5088) → pair (15, 5088)
  12. 16 divides 76320 (76320 ÷ 16 = 4770) → pair (16, 4770)
  13. 18 divides 76320 (76320 ÷ 18 = 4240) → pair (18, 4240)
  14. 20 divides 76320 (76320 ÷ 20 = 3816) → pair (20, 3816)
  15. 24 divides 76320 (76320 ÷ 24 = 3180) → pair (24, 3180)
  16. 30 divides 76320 (76320 ÷ 30 = 2544) → pair (30, 2544)
  17. 32 divides 76320 (76320 ÷ 32 = 2385) → pair (32, 2385)
  18. 36 divides 76320 (76320 ÷ 36 = 2120) → pair (36, 2120)
  19. 40 divides 76320 (76320 ÷ 40 = 1908) → pair (40, 1908)
  20. 45 divides 76320 (76320 ÷ 45 = 1696) → pair (45, 1696)
  21. 48 divides 76320 (76320 ÷ 48 = 1590) → pair (48, 1590)
  22. 53 divides 76320 (76320 ÷ 53 = 1440) → pair (53, 1440)
  23. 60 divides 76320 (76320 ÷ 60 = 1272) → pair (60, 1272)
  24. 72 divides 76320 (76320 ÷ 72 = 1060) → pair (72, 1060)
  25. 80 divides 76320 (76320 ÷ 80 = 954) → pair (80, 954)
  26. 90 divides 76320 (76320 ÷ 90 = 848) → pair (90, 848)
  27. 96 divides 76320 (76320 ÷ 96 = 795) → pair (96, 795)
  28. 106 divides 76320 (76320 ÷ 106 = 720) → pair (106, 720)
  29. 120 divides 76320 (76320 ÷ 120 = 636) → pair (120, 636)
  30. 144 divides 76320 (76320 ÷ 144 = 530) → pair (144, 530)
  31. 159 divides 76320 (76320 ÷ 159 = 480) → pair (159, 480)
  32. 160 divides 76320 (76320 ÷ 160 = 477) → pair (160, 477)
  33. 180 divides 76320 (76320 ÷ 180 = 424) → pair (180, 424)
  34. 212 divides 76320 (76320 ÷ 212 = 360) → pair (212, 360)
  35. 240 divides 76320 (76320 ÷ 240 = 318) → pair (240, 318)
  36. 265 divides 76320 (76320 ÷ 265 = 288) → pair (265, 288)
  37. Collect all unique values: {1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 32, 36, 40, 45, 48, 53, 60, 72, 80, 90, 96, 106, 120, 144, 159, 160, 180, 212, 240, 265, 288, 318, 360, 424, 477, 480, 530, 636, 720, 795, 848, 954, 1060, 1272, 1440, 1590, 1696, 1908, 2120, 2385, 2544, 3180, 3816, 4240, 4770, 5088, 6360, 7632, 8480, 9540, 12720, 15264, 19080, 25440, 38160, 76320} — total 72 divisors.
  38. Sum: 1 + 2 + 3 + 4 + 5 + 6 + 8 + 9 + 10 + 12 + 15 + 16 + 18 + 20 + 24 + 30 + 32 + 36 + 40 + 45 + 48 + 53 + 60 + 72 + 80 + 90 + 96 + 106 + 120 + 144 + 159 + 160 + 180 + 212 + 240 + 265 + 288 + 318 + 360 + 424 + 477 + 480 + 530 + 636 + 720 + 795 + 848 + 954 + 1060 + 1272 + 1440 + 1590 + 1696 + 1908 + 2120 + 2385 + 2544 + 3180 + 3816 + 4240 + 4770 + 5088 + 6360 + 7632 + 8480 + 9540 + 12720 + 15264 + 19080 + 25440 + 38160 + 76320 = 265356.

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See also our tables of divisors:

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

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