Divisors of 31104: All 48 Factors

Divisors (Factors) Calculator

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 31104

The number 31104 has 48 divisors:

1,  2,  3,  4,  6,  8,  9,  12,  16,  18,  24,  27,  32,  36,  48,  54,  64,  72,  81,  96,  108,  128,  144,  162,  192,  216,  243,  288,  324,  384,  432,  486,  576,  648,  864,  972,  1152,  1296,  1728,  1944,  2592,  3456,  3888,  5184,  7776,  10368,  15552,  31104

Divisor Pairs of 31104

Each pair multiplies to 31104:

Number of Divisors

The number 31104 has 48 divisors, written as τ(31104) = 48 in number theory.

Sum of Divisors

σ(31104) = 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 16 + 18 + 24 + 27 + 32 + 36 + 48 + 54 + 64 + 72 + 81 + 96 + 108 + 128 + 144 + 162 + 192 + 216 + 243 + 288 + 324 + 384 + 432 + 486 + 576 + 648 + 864 + 972 + 1152 + 1296 + 1728 + 1944 + 2592 + 3456 + 3888 + 5184 + 7776 + 10368 + 15552 + 31104 = 92820

Prime Factorization of 31104

See the full prime factorization calculator →

Properties of 31104

• 31104 is composite.
• 31104 is not a perfect square.
• Number of divisors: 48.
• Sum of divisors: 92820.

Common Divisors with Another Number?

Looking for the divisors that 31104 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 31104

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √31104 ≈ 176.36. If i divides 31104, then both i and 31104/i are divisors.

1. 1 divides 31104 (31104 ÷ 1 = 31104) → pair (1, 31104)
2. 2 divides 31104 (31104 ÷ 2 = 15552) → pair (2, 15552)
3. 3 divides 31104 (31104 ÷ 3 = 10368) → pair (3, 10368)
4. 4 divides 31104 (31104 ÷ 4 = 7776) → pair (4, 7776)
5. 6 divides 31104 (31104 ÷ 6 = 5184) → pair (6, 5184)
6. 8 divides 31104 (31104 ÷ 8 = 3888) → pair (8, 3888)
7. 9 divides 31104 (31104 ÷ 9 = 3456) → pair (9, 3456)
8. 12 divides 31104 (31104 ÷ 12 = 2592) → pair (12, 2592)
9. 16 divides 31104 (31104 ÷ 16 = 1944) → pair (16, 1944)
10. 18 divides 31104 (31104 ÷ 18 = 1728) → pair (18, 1728)
11. 24 divides 31104 (31104 ÷ 24 = 1296) → pair (24, 1296)
12. 27 divides 31104 (31104 ÷ 27 = 1152) → pair (27, 1152)
13. 32 divides 31104 (31104 ÷ 32 = 972) → pair (32, 972)
14. 36 divides 31104 (31104 ÷ 36 = 864) → pair (36, 864)
15. 48 divides 31104 (31104 ÷ 48 = 648) → pair (48, 648)
16. 54 divides 31104 (31104 ÷ 54 = 576) → pair (54, 576)
17. 64 divides 31104 (31104 ÷ 64 = 486) → pair (64, 486)
18. 72 divides 31104 (31104 ÷ 72 = 432) → pair (72, 432)
19. 81 divides 31104 (31104 ÷ 81 = 384) → pair (81, 384)
20. 96 divides 31104 (31104 ÷ 96 = 324) → pair (96, 324)
21. 108 divides 31104 (31104 ÷ 108 = 288) → pair (108, 288)
22. 128 divides 31104 (31104 ÷ 128 = 243) → pair (128, 243)
23. 144 divides 31104 (31104 ÷ 144 = 216) → pair (144, 216)
24. 162 divides 31104 (31104 ÷ 162 = 192) → pair (162, 192)
25. Collect all unique values: {1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 81, 96, 108, 128, 144, 162, 192, 216, 243, 288, 324, 384, 432, 486, 576, 648, 864, 972, 1152, 1296, 1728, 1944, 2592, 3456, 3888, 5184, 7776, 10368, 15552, 31104} — total 48 divisors.
26. Sum: 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 16 + 18 + 24 + 27 + 32 + 36 + 48 + 54 + 64 + 72 + 81 + 96 + 108 + 128 + 144 + 162 + 192 + 216 + 243 + 288 + 324 + 384 + 432 + 486 + 576 + 648 + 864 + 972 + 1152 + 1296 + 1728 + 1944 + 2592 + 3456 + 3888 + 5184 + 7776 + 10368 + 15552 + 31104 = 92820.

Nearby Examples

Related Operations for 31104

• Multiples of a Number — "outward" complement of divisors
• 31104 Prime Factorization — decompose into prime building blocks
• Find GCF of 31104 and another number
• Find LCM of 31104 and another number
• Is 31104 a perfect square? (odd divisor count ⇔ yes)

See also our tables of divisors:

• Table of all divisors from 1 to 100
• Table of all divisors from 1 to 500
• Table of all divisors from 1 to 1,000
• Table of all divisors from 1 to 10,000

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

• [1] Divisor (Wikipedia)
• [2] Divisor function (Wikipedia)
• [3] Divisor (Wolfram MathWorld)

Divisors Calculation Examples

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