Divisors of 31360: All 48 Factors

Quick Answer

31360 has 48 divisors (factors): 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 32, 35, 40, 49, 56, 64, 70, 80, 98, 112, 128, 140, 160, 196, 224, 245, 280, 320, 392, 448, 490, 560, 640, 784, 896, 980, 1120, 1568, 1960, 2240, 3136, 3920, 4480, 6272, 7840, 15680, 31360.

Sum: 87210.

Divisors (Factors) Calculator

Divisors Multiples Prime Factoriz. GCF LCM

  Ex.: 12, 36, 100, 1024, 1728, etc.
48 divisors
1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 32, 35, 40, 49, 56, 64, 70, 80, 98, 112, 128, 140, 160, 196, 224, 245, 280, 320, 392, 448, 490, 560, 640, 784, 896, 980, 1120, 1568, 1960, 2240, 3136, 3920, 4480, 6272, 7840, 15680, 31360

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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 31360

The number 31360 has 48 divisors:

1,  2,  4,  5,  7,  8,  10,  14,  16,  20,  28,  32,  35,  40,  49,  56,  64,  70,  80,  98,  112,  128,  140,  160,  196,  224,  245,  280,  320,  392,  448,  490,  560,  640,  784,  896,  980,  1120,  1568,  1960,  2240,  3136,  3920,  4480,  6272,  7840,  15680,  31360

Divisor Pairs of 31360

Each pair multiplies to 31360:

Factor 1×Factor 2=Product
1×31360=31360
2×15680=31360
4×7840=31360
5×6272=31360
7×4480=31360
8×3920=31360
10×3136=31360
14×2240=31360
16×1960=31360
20×1568=31360
28×1120=31360
32×980=31360
35×896=31360
40×784=31360
49×640=31360
56×560=31360
64×490=31360
70×448=31360
80×392=31360
98×320=31360
112×280=31360
128×245=31360
140×224=31360
160×196=31360

Number of Divisors

The number 31360 has 48 divisors, written as τ(31360) = 48 in number theory.

Sum of Divisors

σ(31360) = 1 + 2 + 4 + 5 + 7 + 8 + 10 + 14 + 16 + 20 + 28 + 32 + 35 + 40 + 49 + 56 + 64 + 70 + 80 + 98 + 112 + 128 + 140 + 160 + 196 + 224 + 245 + 280 + 320 + 392 + 448 + 490 + 560 + 640 + 784 + 896 + 980 + 1120 + 1568 + 1960 + 2240 + 3136 + 3920 + 4480 + 6272 + 7840 + 15680 + 31360 = 87210

Prime Factorization of 31360

See the full prime factorization calculator →

Properties of 31360

  • 31360 is composite.
  • 31360 is not a perfect square.
  • Number of divisors: 48.
  • Sum of divisors: 87210.

Common Divisors with Another Number?

Looking for the divisors that 31360 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 31360

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √31360 ≈ 177.09. If i divides 31360, then both i and 31360/i are divisors.

  1. 1 divides 31360 (31360 ÷ 1 = 31360) → pair (1, 31360)
  2. 2 divides 31360 (31360 ÷ 2 = 15680) → pair (2, 15680)
  3. 4 divides 31360 (31360 ÷ 4 = 7840) → pair (4, 7840)
  4. 5 divides 31360 (31360 ÷ 5 = 6272) → pair (5, 6272)
  5. 7 divides 31360 (31360 ÷ 7 = 4480) → pair (7, 4480)
  6. 8 divides 31360 (31360 ÷ 8 = 3920) → pair (8, 3920)
  7. 10 divides 31360 (31360 ÷ 10 = 3136) → pair (10, 3136)
  8. 14 divides 31360 (31360 ÷ 14 = 2240) → pair (14, 2240)
  9. 16 divides 31360 (31360 ÷ 16 = 1960) → pair (16, 1960)
  10. 20 divides 31360 (31360 ÷ 20 = 1568) → pair (20, 1568)
  11. 28 divides 31360 (31360 ÷ 28 = 1120) → pair (28, 1120)
  12. 32 divides 31360 (31360 ÷ 32 = 980) → pair (32, 980)
  13. 35 divides 31360 (31360 ÷ 35 = 896) → pair (35, 896)
  14. 40 divides 31360 (31360 ÷ 40 = 784) → pair (40, 784)
  15. 49 divides 31360 (31360 ÷ 49 = 640) → pair (49, 640)
  16. 56 divides 31360 (31360 ÷ 56 = 560) → pair (56, 560)
  17. 64 divides 31360 (31360 ÷ 64 = 490) → pair (64, 490)
  18. 70 divides 31360 (31360 ÷ 70 = 448) → pair (70, 448)
  19. 80 divides 31360 (31360 ÷ 80 = 392) → pair (80, 392)
  20. 98 divides 31360 (31360 ÷ 98 = 320) → pair (98, 320)
  21. 112 divides 31360 (31360 ÷ 112 = 280) → pair (112, 280)
  22. 128 divides 31360 (31360 ÷ 128 = 245) → pair (128, 245)
  23. 140 divides 31360 (31360 ÷ 140 = 224) → pair (140, 224)
  24. 160 divides 31360 (31360 ÷ 160 = 196) → pair (160, 196)
  25. Collect all unique values: {1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 32, 35, 40, 49, 56, 64, 70, 80, 98, 112, 128, 140, 160, 196, 224, 245, 280, 320, 392, 448, 490, 560, 640, 784, 896, 980, 1120, 1568, 1960, 2240, 3136, 3920, 4480, 6272, 7840, 15680, 31360} — total 48 divisors.
  26. Sum: 1 + 2 + 4 + 5 + 7 + 8 + 10 + 14 + 16 + 20 + 28 + 32 + 35 + 40 + 49 + 56 + 64 + 70 + 80 + 98 + 112 + 128 + 140 + 160 + 196 + 224 + 245 + 280 + 320 + 392 + 448 + 490 + 560 + 640 + 784 + 896 + 980 + 1120 + 1568 + 1960 + 2240 + 3136 + 3920 + 4480 + 6272 + 7840 + 15680 + 31360 = 87210.

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Related Operations for 31360

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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