Divisors of 37920: All 48 Factors

Quick Answer

37920 has 48 divisors (factors): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 79, 80, 96, 120, 158, 160, 237, 240, 316, 395, 474, 480, 632, 790, 948, 1185, 1264, 1580, 1896, 2370, 2528, 3160, 3792, 4740, 6320, 7584, 9480, 12640, 18960, 37920.

Sum: 120960.

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, 40, 48, 60, 79, 80, 96, 120, 158, 160, 237, 240, 316, 395, 474, 480, 632, 790, 948, 1185, 1264, 1580, 1896, 2370, 2528, 3160, 3792, 4740, 6320, 7584, 9480, 12640, 18960, 37920

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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 37920

The number 37920 has 48 divisors:

1,  2,  3,  4,  5,  6,  8,  10,  12,  15,  16,  20,  24,  30,  32,  40,  48,  60,  79,  80,  96,  120,  158,  160,  237,  240,  316,  395,  474,  480,  632,  790,  948,  1185,  1264,  1580,  1896,  2370,  2528,  3160,  3792,  4740,  6320,  7584,  9480,  12640,  18960,  37920

Divisor Pairs of 37920

Each pair multiplies to 37920:

Factor 1×Factor 2=Product
1×37920=37920
2×18960=37920
3×12640=37920
4×9480=37920
5×7584=37920
6×6320=37920
8×4740=37920
10×3792=37920
12×3160=37920
15×2528=37920
16×2370=37920
20×1896=37920
24×1580=37920
30×1264=37920
32×1185=37920
40×948=37920
48×790=37920
60×632=37920
79×480=37920
80×474=37920
96×395=37920
120×316=37920
158×240=37920
160×237=37920

Number of Divisors

The number 37920 has 48 divisors, written as τ(37920) = 48 in number theory.

Sum of Divisors

σ(37920) = 1 + 2 + 3 + 4 + 5 + 6 + 8 + 10 + 12 + 15 + 16 + 20 + 24 + 30 + 32 + 40 + 48 + 60 + 79 + 80 + 96 + 120 + 158 + 160 + 237 + 240 + 316 + 395 + 474 + 480 + 632 + 790 + 948 + 1185 + 1264 + 1580 + 1896 + 2370 + 2528 + 3160 + 3792 + 4740 + 6320 + 7584 + 9480 + 12640 + 18960 + 37920 = 120960

Prime Factorization of 37920

See the full prime factorization calculator →

Properties of 37920

  • 37920 is composite.
  • 37920 is not a perfect square.
  • Number of divisors: 48.
  • Sum of divisors: 120960.

Common Divisors with Another Number?

Looking for the divisors that 37920 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 37920

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √37920 ≈ 194.73. If i divides 37920, then both i and 37920/i are divisors.

  1. 1 divides 37920 (37920 ÷ 1 = 37920) → pair (1, 37920)
  2. 2 divides 37920 (37920 ÷ 2 = 18960) → pair (2, 18960)
  3. 3 divides 37920 (37920 ÷ 3 = 12640) → pair (3, 12640)
  4. 4 divides 37920 (37920 ÷ 4 = 9480) → pair (4, 9480)
  5. 5 divides 37920 (37920 ÷ 5 = 7584) → pair (5, 7584)
  6. 6 divides 37920 (37920 ÷ 6 = 6320) → pair (6, 6320)
  7. 8 divides 37920 (37920 ÷ 8 = 4740) → pair (8, 4740)
  8. 10 divides 37920 (37920 ÷ 10 = 3792) → pair (10, 3792)
  9. 12 divides 37920 (37920 ÷ 12 = 3160) → pair (12, 3160)
  10. 15 divides 37920 (37920 ÷ 15 = 2528) → pair (15, 2528)
  11. 16 divides 37920 (37920 ÷ 16 = 2370) → pair (16, 2370)
  12. 20 divides 37920 (37920 ÷ 20 = 1896) → pair (20, 1896)
  13. 24 divides 37920 (37920 ÷ 24 = 1580) → pair (24, 1580)
  14. 30 divides 37920 (37920 ÷ 30 = 1264) → pair (30, 1264)
  15. 32 divides 37920 (37920 ÷ 32 = 1185) → pair (32, 1185)
  16. 40 divides 37920 (37920 ÷ 40 = 948) → pair (40, 948)
  17. 48 divides 37920 (37920 ÷ 48 = 790) → pair (48, 790)
  18. 60 divides 37920 (37920 ÷ 60 = 632) → pair (60, 632)
  19. 79 divides 37920 (37920 ÷ 79 = 480) → pair (79, 480)
  20. 80 divides 37920 (37920 ÷ 80 = 474) → pair (80, 474)
  21. 96 divides 37920 (37920 ÷ 96 = 395) → pair (96, 395)
  22. 120 divides 37920 (37920 ÷ 120 = 316) → pair (120, 316)
  23. 158 divides 37920 (37920 ÷ 158 = 240) → pair (158, 240)
  24. 160 divides 37920 (37920 ÷ 160 = 237) → pair (160, 237)
  25. Collect all unique values: {1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 79, 80, 96, 120, 158, 160, 237, 240, 316, 395, 474, 480, 632, 790, 948, 1185, 1264, 1580, 1896, 2370, 2528, 3160, 3792, 4740, 6320, 7584, 9480, 12640, 18960, 37920} — total 48 divisors.
  26. Sum: 1 + 2 + 3 + 4 + 5 + 6 + 8 + 10 + 12 + 15 + 16 + 20 + 24 + 30 + 32 + 40 + 48 + 60 + 79 + 80 + 96 + 120 + 158 + 160 + 237 + 240 + 316 + 395 + 474 + 480 + 632 + 790 + 948 + 1185 + 1264 + 1580 + 1896 + 2370 + 2528 + 3160 + 3792 + 4740 + 6320 + 7584 + 9480 + 12640 + 18960 + 37920 = 120960.

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Related Operations for 37920

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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