Divisors of 23520: All 72 Factors

Quick Answer

23520 has 72 divisors (factors): 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 32, 35, 40, 42, 48, 49, 56, 60, 70, 80, 84, 96, 98, 105, 112, 120, 140, 147, 160, 168, 196, 210, 224, 240, 245, 280, 294, 336, 392, 420, 480, 490, 560, 588, 672, 735, 784, 840, 980, 1120, 1176, 1470, 1568, 1680, 1960, 2352, 2940, 3360, 3920, 4704, 5880, 7840, 11760, 23520.

Sum: 86184.

Divisors (Factors) Calculator

Divisors Multiples Prime Factoriz. GCF LCM

  Ex.: 12, 36, 100, 1024, 1728, etc.
72 divisors
1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 32, 35, 40, 42, 48, 49, 56, 60, 70, 80, 84, 96, 98, 105, 112, 120, 140, 147, 160, 168, 196, 210, 224, 240, 245, 280, 294, 336, 392, 420, 480, 490, 560, 588, 672, 735, 784, 840, 980, 1120, 1176, 1470, 1568, 1680, 1960, 2352, 2940, 3360, 3920, 4704, 5880, 7840, 11760, 23520

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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 23520

The number 23520 has 72 divisors:

1,  2,  3,  4,  5,  6,  7,  8,  10,  12,  14,  15,  16,  20,  21,  24,  28,  30,  32,  35,  40,  42,  48,  49,  56,  60,  70,  80,  84,  96,  98,  105,  112,  120,  140,  147,  160,  168,  196,  210,  224,  240,  245,  280,  294,  336,  392,  420,  480,  490,  560,  588,  672,  735,  784,  840,  980,  1120,  1176,  1470,  1568,  1680,  1960,  2352,  2940,  3360,  3920,  4704,  5880,  7840,  11760,  23520

Divisor Pairs of 23520

Each pair multiplies to 23520:

Factor 1×Factor 2=Product
1×23520=23520
2×11760=23520
3×7840=23520
4×5880=23520
5×4704=23520
6×3920=23520
7×3360=23520
8×2940=23520
10×2352=23520
12×1960=23520
14×1680=23520
15×1568=23520
16×1470=23520
20×1176=23520
21×1120=23520
24×980=23520
28×840=23520
30×784=23520
32×735=23520
35×672=23520
40×588=23520
42×560=23520
48×490=23520
49×480=23520
56×420=23520
60×392=23520
70×336=23520
80×294=23520
84×280=23520
96×245=23520
98×240=23520
105×224=23520
112×210=23520
120×196=23520
140×168=23520
147×160=23520

Number of Divisors

The number 23520 has 72 divisors, written as τ(23520) = 72 in number theory.

Sum of Divisors

σ(23520) = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 10 + 12 + 14 + 15 + 16 + 20 + 21 + 24 + 28 + 30 + 32 + 35 + 40 + 42 + 48 + 49 + 56 + 60 + 70 + 80 + 84 + 96 + 98 + 105 + 112 + 120 + 140 + 147 + 160 + 168 + 196 + 210 + 224 + 240 + 245 + 280 + 294 + 336 + 392 + 420 + 480 + 490 + 560 + 588 + 672 + 735 + 784 + 840 + 980 + 1120 + 1176 + 1470 + 1568 + 1680 + 1960 + 2352 + 2940 + 3360 + 3920 + 4704 + 5880 + 7840 + 11760 + 23520 = 86184

Prime Factorization of 23520

See the full prime factorization calculator →

Properties of 23520

  • 23520 is composite.
  • 23520 is not a perfect square.
  • Number of divisors: 72.
  • Sum of divisors: 86184.

Common Divisors with Another Number?

Looking for the divisors that 23520 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 23520

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √23520 ≈ 153.36. If i divides 23520, then both i and 23520/i are divisors.

  1. 1 divides 23520 (23520 ÷ 1 = 23520) → pair (1, 23520)
  2. 2 divides 23520 (23520 ÷ 2 = 11760) → pair (2, 11760)
  3. 3 divides 23520 (23520 ÷ 3 = 7840) → pair (3, 7840)
  4. 4 divides 23520 (23520 ÷ 4 = 5880) → pair (4, 5880)
  5. 5 divides 23520 (23520 ÷ 5 = 4704) → pair (5, 4704)
  6. 6 divides 23520 (23520 ÷ 6 = 3920) → pair (6, 3920)
  7. 7 divides 23520 (23520 ÷ 7 = 3360) → pair (7, 3360)
  8. 8 divides 23520 (23520 ÷ 8 = 2940) → pair (8, 2940)
  9. 10 divides 23520 (23520 ÷ 10 = 2352) → pair (10, 2352)
  10. 12 divides 23520 (23520 ÷ 12 = 1960) → pair (12, 1960)
  11. 14 divides 23520 (23520 ÷ 14 = 1680) → pair (14, 1680)
  12. 15 divides 23520 (23520 ÷ 15 = 1568) → pair (15, 1568)
  13. 16 divides 23520 (23520 ÷ 16 = 1470) → pair (16, 1470)
  14. 20 divides 23520 (23520 ÷ 20 = 1176) → pair (20, 1176)
  15. 21 divides 23520 (23520 ÷ 21 = 1120) → pair (21, 1120)
  16. 24 divides 23520 (23520 ÷ 24 = 980) → pair (24, 980)
  17. 28 divides 23520 (23520 ÷ 28 = 840) → pair (28, 840)
  18. 30 divides 23520 (23520 ÷ 30 = 784) → pair (30, 784)
  19. 32 divides 23520 (23520 ÷ 32 = 735) → pair (32, 735)
  20. 35 divides 23520 (23520 ÷ 35 = 672) → pair (35, 672)
  21. 40 divides 23520 (23520 ÷ 40 = 588) → pair (40, 588)
  22. 42 divides 23520 (23520 ÷ 42 = 560) → pair (42, 560)
  23. 48 divides 23520 (23520 ÷ 48 = 490) → pair (48, 490)
  24. 49 divides 23520 (23520 ÷ 49 = 480) → pair (49, 480)
  25. 56 divides 23520 (23520 ÷ 56 = 420) → pair (56, 420)
  26. 60 divides 23520 (23520 ÷ 60 = 392) → pair (60, 392)
  27. 70 divides 23520 (23520 ÷ 70 = 336) → pair (70, 336)
  28. 80 divides 23520 (23520 ÷ 80 = 294) → pair (80, 294)
  29. 84 divides 23520 (23520 ÷ 84 = 280) → pair (84, 280)
  30. 96 divides 23520 (23520 ÷ 96 = 245) → pair (96, 245)
  31. 98 divides 23520 (23520 ÷ 98 = 240) → pair (98, 240)
  32. 105 divides 23520 (23520 ÷ 105 = 224) → pair (105, 224)
  33. 112 divides 23520 (23520 ÷ 112 = 210) → pair (112, 210)
  34. 120 divides 23520 (23520 ÷ 120 = 196) → pair (120, 196)
  35. 140 divides 23520 (23520 ÷ 140 = 168) → pair (140, 168)
  36. 147 divides 23520 (23520 ÷ 147 = 160) → pair (147, 160)
  37. Collect all unique values: {1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 32, 35, 40, 42, 48, 49, 56, 60, 70, 80, 84, 96, 98, 105, 112, 120, 140, 147, 160, 168, 196, 210, 224, 240, 245, 280, 294, 336, 392, 420, 480, 490, 560, 588, 672, 735, 784, 840, 980, 1120, 1176, 1470, 1568, 1680, 1960, 2352, 2940, 3360, 3920, 4704, 5880, 7840, 11760, 23520} — total 72 divisors.
  38. Sum: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 10 + 12 + 14 + 15 + 16 + 20 + 21 + 24 + 28 + 30 + 32 + 35 + 40 + 42 + 48 + 49 + 56 + 60 + 70 + 80 + 84 + 96 + 98 + 105 + 112 + 120 + 140 + 147 + 160 + 168 + 196 + 210 + 224 + 240 + 245 + 280 + 294 + 336 + 392 + 420 + 480 + 490 + 560 + 588 + 672 + 735 + 784 + 840 + 980 + 1120 + 1176 + 1470 + 1568 + 1680 + 1960 + 2352 + 2940 + 3360 + 3920 + 4704 + 5880 + 7840 + 11760 + 23520 = 86184.

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Related Operations for 23520

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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