Divisors of 17760: All 48 Factors

Quick Answer

17760 has 48 divisors (factors): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 37, 40, 48, 60, 74, 80, 96, 111, 120, 148, 160, 185, 222, 240, 296, 370, 444, 480, 555, 592, 740, 888, 1110, 1184, 1480, 1776, 2220, 2960, 3552, 4440, 5920, 8880, 17760.

Sum: 57456.

Divisors (Factors) Calculator

Divisors Multiples Prime Factoriz. GCF LCM

  Ex.: 12, 36, 100, 1024, 1728, etc.
48 divisors
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 37, 40, 48, 60, 74, 80, 96, 111, 120, 148, 160, 185, 222, 240, 296, 370, 444, 480, 555, 592, 740, 888, 1110, 1184, 1480, 1776, 2220, 2960, 3552, 4440, 5920, 8880, 17760

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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 17760

The number 17760 has 48 divisors:

1,  2,  3,  4,  5,  6,  8,  10,  12,  15,  16,  20,  24,  30,  32,  37,  40,  48,  60,  74,  80,  96,  111,  120,  148,  160,  185,  222,  240,  296,  370,  444,  480,  555,  592,  740,  888,  1110,  1184,  1480,  1776,  2220,  2960,  3552,  4440,  5920,  8880,  17760

Divisor Pairs of 17760

Each pair multiplies to 17760:

Factor 1×Factor 2=Product
1×17760=17760
2×8880=17760
3×5920=17760
4×4440=17760
5×3552=17760
6×2960=17760
8×2220=17760
10×1776=17760
12×1480=17760
15×1184=17760
16×1110=17760
20×888=17760
24×740=17760
30×592=17760
32×555=17760
37×480=17760
40×444=17760
48×370=17760
60×296=17760
74×240=17760
80×222=17760
96×185=17760
111×160=17760
120×148=17760

Number of Divisors

The number 17760 has 48 divisors, written as τ(17760) = 48 in number theory.

Sum of Divisors

σ(17760) = 1 + 2 + 3 + 4 + 5 + 6 + 8 + 10 + 12 + 15 + 16 + 20 + 24 + 30 + 32 + 37 + 40 + 48 + 60 + 74 + 80 + 96 + 111 + 120 + 148 + 160 + 185 + 222 + 240 + 296 + 370 + 444 + 480 + 555 + 592 + 740 + 888 + 1110 + 1184 + 1480 + 1776 + 2220 + 2960 + 3552 + 4440 + 5920 + 8880 + 17760 = 57456

Prime Factorization of 17760

See the full prime factorization calculator →

Properties of 17760

  • 17760 is composite.
  • 17760 is not a perfect square.
  • Number of divisors: 48.
  • Sum of divisors: 57456.

Common Divisors with Another Number?

Looking for the divisors that 17760 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 17760

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √17760 ≈ 133.27. If i divides 17760, then both i and 17760/i are divisors.

  1. 1 divides 17760 (17760 ÷ 1 = 17760) → pair (1, 17760)
  2. 2 divides 17760 (17760 ÷ 2 = 8880) → pair (2, 8880)
  3. 3 divides 17760 (17760 ÷ 3 = 5920) → pair (3, 5920)
  4. 4 divides 17760 (17760 ÷ 4 = 4440) → pair (4, 4440)
  5. 5 divides 17760 (17760 ÷ 5 = 3552) → pair (5, 3552)
  6. 6 divides 17760 (17760 ÷ 6 = 2960) → pair (6, 2960)
  7. 8 divides 17760 (17760 ÷ 8 = 2220) → pair (8, 2220)
  8. 10 divides 17760 (17760 ÷ 10 = 1776) → pair (10, 1776)
  9. 12 divides 17760 (17760 ÷ 12 = 1480) → pair (12, 1480)
  10. 15 divides 17760 (17760 ÷ 15 = 1184) → pair (15, 1184)
  11. 16 divides 17760 (17760 ÷ 16 = 1110) → pair (16, 1110)
  12. 20 divides 17760 (17760 ÷ 20 = 888) → pair (20, 888)
  13. 24 divides 17760 (17760 ÷ 24 = 740) → pair (24, 740)
  14. 30 divides 17760 (17760 ÷ 30 = 592) → pair (30, 592)
  15. 32 divides 17760 (17760 ÷ 32 = 555) → pair (32, 555)
  16. 37 divides 17760 (17760 ÷ 37 = 480) → pair (37, 480)
  17. 40 divides 17760 (17760 ÷ 40 = 444) → pair (40, 444)
  18. 48 divides 17760 (17760 ÷ 48 = 370) → pair (48, 370)
  19. 60 divides 17760 (17760 ÷ 60 = 296) → pair (60, 296)
  20. 74 divides 17760 (17760 ÷ 74 = 240) → pair (74, 240)
  21. 80 divides 17760 (17760 ÷ 80 = 222) → pair (80, 222)
  22. 96 divides 17760 (17760 ÷ 96 = 185) → pair (96, 185)
  23. 111 divides 17760 (17760 ÷ 111 = 160) → pair (111, 160)
  24. 120 divides 17760 (17760 ÷ 120 = 148) → pair (120, 148)
  25. Collect all unique values: {1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 37, 40, 48, 60, 74, 80, 96, 111, 120, 148, 160, 185, 222, 240, 296, 370, 444, 480, 555, 592, 740, 888, 1110, 1184, 1480, 1776, 2220, 2960, 3552, 4440, 5920, 8880, 17760} — total 48 divisors.
  26. Sum: 1 + 2 + 3 + 4 + 5 + 6 + 8 + 10 + 12 + 15 + 16 + 20 + 24 + 30 + 32 + 37 + 40 + 48 + 60 + 74 + 80 + 96 + 111 + 120 + 148 + 160 + 185 + 222 + 240 + 296 + 370 + 444 + 480 + 555 + 592 + 740 + 888 + 1110 + 1184 + 1480 + 1776 + 2220 + 2960 + 3552 + 4440 + 5920 + 8880 + 17760 = 57456.

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Related Operations for 17760

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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