Divisors of 34560: All 72 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 34560

The number 34560 has 72 divisors:

1,  2,  3,  4,  5,  6,  8,  9,  10,  12,  15,  16,  18,  20,  24,  27,  30,  32,  36,  40,  45,  48,  54,  60,  64,  72,  80,  90,  96,  108,  120,  128,  135,  144,  160,  180,  192,  216,  240,  256,  270,  288,  320,  360,  384,  432,  480,  540,  576,  640,  720,  768,  864,  960,  1080,  1152,  1280,  1440,  1728,  1920,  2160,  2304,  2880,  3456,  3840,  4320,  5760,  6912,  8640,  11520,  17280,  34560

Divisor Pairs of 34560

Each pair multiplies to 34560:

Number of Divisors

The number 34560 has 72 divisors, written as τ(34560) = 72 in number theory.

Sum of Divisors

σ(34560) = 1 + 2 + 3 + 4 + 5 + 6 + 8 + 9 + 10 + 12 + 15 + 16 + 18 + 20 + 24 + 27 + 30 + 32 + 36 + 40 + 45 + 48 + 54 + 60 + 64 + 72 + 80 + 90 + 96 + 108 + 120 + 128 + 135 + 144 + 160 + 180 + 192 + 216 + 240 + 256 + 270 + 288 + 320 + 360 + 384 + 432 + 480 + 540 + 576 + 640 + 720 + 768 + 864 + 960 + 1080 + 1152 + 1280 + 1440 + 1728 + 1920 + 2160 + 2304 + 2880 + 3456 + 3840 + 4320 + 5760 + 6912 + 8640 + 11520 + 17280 + 34560 = 122640

Prime Factorization of 34560

See the full prime factorization calculator →

Properties of 34560

• 34560 is composite.
• 34560 is not a perfect square.
• Number of divisors: 72.
• Sum of divisors: 122640.

Common Divisors with Another Number?

Looking for the divisors that 34560 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 34560

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √34560 ≈ 185.90. If i divides 34560, then both i and 34560/i are divisors.

1. 1 divides 34560 (34560 ÷ 1 = 34560) → pair (1, 34560)
2. 2 divides 34560 (34560 ÷ 2 = 17280) → pair (2, 17280)
3. 3 divides 34560 (34560 ÷ 3 = 11520) → pair (3, 11520)
4. 4 divides 34560 (34560 ÷ 4 = 8640) → pair (4, 8640)
5. 5 divides 34560 (34560 ÷ 5 = 6912) → pair (5, 6912)
6. 6 divides 34560 (34560 ÷ 6 = 5760) → pair (6, 5760)
7. 8 divides 34560 (34560 ÷ 8 = 4320) → pair (8, 4320)
8. 9 divides 34560 (34560 ÷ 9 = 3840) → pair (9, 3840)
9. 10 divides 34560 (34560 ÷ 10 = 3456) → pair (10, 3456)
10. 12 divides 34560 (34560 ÷ 12 = 2880) → pair (12, 2880)
11. 15 divides 34560 (34560 ÷ 15 = 2304) → pair (15, 2304)
12. 16 divides 34560 (34560 ÷ 16 = 2160) → pair (16, 2160)
13. 18 divides 34560 (34560 ÷ 18 = 1920) → pair (18, 1920)
14. 20 divides 34560 (34560 ÷ 20 = 1728) → pair (20, 1728)
15. 24 divides 34560 (34560 ÷ 24 = 1440) → pair (24, 1440)
16. 27 divides 34560 (34560 ÷ 27 = 1280) → pair (27, 1280)
17. 30 divides 34560 (34560 ÷ 30 = 1152) → pair (30, 1152)
18. 32 divides 34560 (34560 ÷ 32 = 1080) → pair (32, 1080)
19. 36 divides 34560 (34560 ÷ 36 = 960) → pair (36, 960)
20. 40 divides 34560 (34560 ÷ 40 = 864) → pair (40, 864)
21. 45 divides 34560 (34560 ÷ 45 = 768) → pair (45, 768)
22. 48 divides 34560 (34560 ÷ 48 = 720) → pair (48, 720)
23. 54 divides 34560 (34560 ÷ 54 = 640) → pair (54, 640)
24. 60 divides 34560 (34560 ÷ 60 = 576) → pair (60, 576)
25. 64 divides 34560 (34560 ÷ 64 = 540) → pair (64, 540)
26. 72 divides 34560 (34560 ÷ 72 = 480) → pair (72, 480)
27. 80 divides 34560 (34560 ÷ 80 = 432) → pair (80, 432)
28. 90 divides 34560 (34560 ÷ 90 = 384) → pair (90, 384)
29. 96 divides 34560 (34560 ÷ 96 = 360) → pair (96, 360)
30. 108 divides 34560 (34560 ÷ 108 = 320) → pair (108, 320)
31. 120 divides 34560 (34560 ÷ 120 = 288) → pair (120, 288)
32. 128 divides 34560 (34560 ÷ 128 = 270) → pair (128, 270)
33. 135 divides 34560 (34560 ÷ 135 = 256) → pair (135, 256)
34. 144 divides 34560 (34560 ÷ 144 = 240) → pair (144, 240)
35. 160 divides 34560 (34560 ÷ 160 = 216) → pair (160, 216)
36. 180 divides 34560 (34560 ÷ 180 = 192) → pair (180, 192)
37. Collect all unique values: {1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 27, 30, 32, 36, 40, 45, 48, 54, 60, 64, 72, 80, 90, 96, 108, 120, 128, 135, 144, 160, 180, 192, 216, 240, 256, 270, 288, 320, 360, 384, 432, 480, 540, 576, 640, 720, 768, 864, 960, 1080, 1152, 1280, 1440, 1728, 1920, 2160, 2304, 2880, 3456, 3840, 4320, 5760, 6912, 8640, 11520, 17280, 34560} — total 72 divisors.
38. Sum: 1 + 2 + 3 + 4 + 5 + 6 + 8 + 9 + 10 + 12 + 15 + 16 + 18 + 20 + 24 + 27 + 30 + 32 + 36 + 40 + 45 + 48 + 54 + 60 + 64 + 72 + 80 + 90 + 96 + 108 + 120 + 128 + 135 + 144 + 160 + 180 + 192 + 216 + 240 + 256 + 270 + 288 + 320 + 360 + 384 + 432 + 480 + 540 + 576 + 640 + 720 + 768 + 864 + 960 + 1080 + 1152 + 1280 + 1440 + 1728 + 1920 + 2160 + 2304 + 2880 + 3456 + 3840 + 4320 + 5760 + 6912 + 8640 + 11520 + 17280 + 34560 = 122640.

Nearby Examples

Related Operations for 34560

• Multiples of a Number — "outward" complement of divisors
• 34560 Prime Factorization — decompose into prime building blocks
• Find GCF of 34560 and another number
• Find LCM of 34560 and another number
• Is 34560 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

Find all divisors of these numbers: