Divisors of 31590: All 48 Factors

Quick Answer

31590 has 48 divisors (factors): 1, 2, 3, 5, 6, 9, 10, 13, 15, 18, 26, 27, 30, 39, 45, 54, 65, 78, 81, 90, 117, 130, 135, 162, 195, 234, 243, 270, 351, 390, 405, 486, 585, 702, 810, 1053, 1170, 1215, 1755, 2106, 2430, 3159, 3510, 5265, 6318, 10530, 15795, 31590.

Sum: 91728.

Divisors (Factors) Calculator

Divisors Multiples Prime Factoriz. GCF LCM

  Ex.: 12, 36, 100, 1024, 1728, etc.
48 divisors
1, 2, 3, 5, 6, 9, 10, 13, 15, 18, 26, 27, 30, 39, 45, 54, 65, 78, 81, 90, 117, 130, 135, 162, 195, 234, 243, 270, 351, 390, 405, 486, 585, 702, 810, 1053, 1170, 1215, 1755, 2106, 2430, 3159, 3510, 5265, 6318, 10530, 15795, 31590

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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 31590

The number 31590 has 48 divisors:

1,  2,  3,  5,  6,  9,  10,  13,  15,  18,  26,  27,  30,  39,  45,  54,  65,  78,  81,  90,  117,  130,  135,  162,  195,  234,  243,  270,  351,  390,  405,  486,  585,  702,  810,  1053,  1170,  1215,  1755,  2106,  2430,  3159,  3510,  5265,  6318,  10530,  15795,  31590

Divisor Pairs of 31590

Each pair multiplies to 31590:

Factor 1×Factor 2=Product
1×31590=31590
2×15795=31590
3×10530=31590
5×6318=31590
6×5265=31590
9×3510=31590
10×3159=31590
13×2430=31590
15×2106=31590
18×1755=31590
26×1215=31590
27×1170=31590
30×1053=31590
39×810=31590
45×702=31590
54×585=31590
65×486=31590
78×405=31590
81×390=31590
90×351=31590
117×270=31590
130×243=31590
135×234=31590
162×195=31590

Number of Divisors

The number 31590 has 48 divisors, written as τ(31590) = 48 in number theory.

Sum of Divisors

σ(31590) = 1 + 2 + 3 + 5 + 6 + 9 + 10 + 13 + 15 + 18 + 26 + 27 + 30 + 39 + 45 + 54 + 65 + 78 + 81 + 90 + 117 + 130 + 135 + 162 + 195 + 234 + 243 + 270 + 351 + 390 + 405 + 486 + 585 + 702 + 810 + 1053 + 1170 + 1215 + 1755 + 2106 + 2430 + 3159 + 3510 + 5265 + 6318 + 10530 + 15795 + 31590 = 91728

Prime Factorization of 31590

See the full prime factorization calculator →

Properties of 31590

  • 31590 is composite.
  • 31590 is not a perfect square.
  • Number of divisors: 48.
  • Sum of divisors: 91728.

Common Divisors with Another Number?

Looking for the divisors that 31590 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 31590

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √31590 ≈ 177.74. If i divides 31590, then both i and 31590/i are divisors.

  1. 1 divides 31590 (31590 ÷ 1 = 31590) → pair (1, 31590)
  2. 2 divides 31590 (31590 ÷ 2 = 15795) → pair (2, 15795)
  3. 3 divides 31590 (31590 ÷ 3 = 10530) → pair (3, 10530)
  4. 5 divides 31590 (31590 ÷ 5 = 6318) → pair (5, 6318)
  5. 6 divides 31590 (31590 ÷ 6 = 5265) → pair (6, 5265)
  6. 9 divides 31590 (31590 ÷ 9 = 3510) → pair (9, 3510)
  7. 10 divides 31590 (31590 ÷ 10 = 3159) → pair (10, 3159)
  8. 13 divides 31590 (31590 ÷ 13 = 2430) → pair (13, 2430)
  9. 15 divides 31590 (31590 ÷ 15 = 2106) → pair (15, 2106)
  10. 18 divides 31590 (31590 ÷ 18 = 1755) → pair (18, 1755)
  11. 26 divides 31590 (31590 ÷ 26 = 1215) → pair (26, 1215)
  12. 27 divides 31590 (31590 ÷ 27 = 1170) → pair (27, 1170)
  13. 30 divides 31590 (31590 ÷ 30 = 1053) → pair (30, 1053)
  14. 39 divides 31590 (31590 ÷ 39 = 810) → pair (39, 810)
  15. 45 divides 31590 (31590 ÷ 45 = 702) → pair (45, 702)
  16. 54 divides 31590 (31590 ÷ 54 = 585) → pair (54, 585)
  17. 65 divides 31590 (31590 ÷ 65 = 486) → pair (65, 486)
  18. 78 divides 31590 (31590 ÷ 78 = 405) → pair (78, 405)
  19. 81 divides 31590 (31590 ÷ 81 = 390) → pair (81, 390)
  20. 90 divides 31590 (31590 ÷ 90 = 351) → pair (90, 351)
  21. 117 divides 31590 (31590 ÷ 117 = 270) → pair (117, 270)
  22. 130 divides 31590 (31590 ÷ 130 = 243) → pair (130, 243)
  23. 135 divides 31590 (31590 ÷ 135 = 234) → pair (135, 234)
  24. 162 divides 31590 (31590 ÷ 162 = 195) → pair (162, 195)
  25. Collect all unique values: {1, 2, 3, 5, 6, 9, 10, 13, 15, 18, 26, 27, 30, 39, 45, 54, 65, 78, 81, 90, 117, 130, 135, 162, 195, 234, 243, 270, 351, 390, 405, 486, 585, 702, 810, 1053, 1170, 1215, 1755, 2106, 2430, 3159, 3510, 5265, 6318, 10530, 15795, 31590} — total 48 divisors.
  26. Sum: 1 + 2 + 3 + 5 + 6 + 9 + 10 + 13 + 15 + 18 + 26 + 27 + 30 + 39 + 45 + 54 + 65 + 78 + 81 + 90 + 117 + 130 + 135 + 162 + 195 + 234 + 243 + 270 + 351 + 390 + 405 + 486 + 585 + 702 + 810 + 1053 + 1170 + 1215 + 1755 + 2106 + 2430 + 3159 + 3510 + 5265 + 6318 + 10530 + 15795 + 31590 = 91728.

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Related Operations for 31590

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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