Divisors of 36120: All 64 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 36120

The number 36120 has 64 divisors:

1,  2,  3,  4,  5,  6,  7,  8,  10,  12,  14,  15,  20,  21,  24,  28,  30,  35,  40,  42,  43,  56,  60,  70,  84,  86,  105,  120,  129,  140,  168,  172,  210,  215,  258,  280,  301,  344,  420,  430,  516,  602,  645,  840,  860,  903,  1032,  1204,  1290,  1505,  1720,  1806,  2408,  2580,  3010,  3612,  4515,  5160,  6020,  7224,  9030,  12040,  18060,  36120

Divisor Pairs of 36120

Each pair multiplies to 36120:

Number of Divisors

The number 36120 has 64 divisors, written as τ(36120) = 64 in number theory.

Sum of Divisors

σ(36120) = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 10 + 12 + 14 + 15 + 20 + 21 + 24 + 28 + 30 + 35 + 40 + 42 + 43 + 56 + 60 + 70 + 84 + 86 + 105 + 120 + 129 + 140 + 168 + 172 + 210 + 215 + 258 + 280 + 301 + 344 + 420 + 430 + 516 + 602 + 645 + 840 + 860 + 903 + 1032 + 1204 + 1290 + 1505 + 1720 + 1806 + 2408 + 2580 + 3010 + 3612 + 4515 + 5160 + 6020 + 7224 + 9030 + 12040 + 18060 + 36120 = 126720

Prime Factorization of 36120

See the full prime factorization calculator →

Properties of 36120

• 36120 is composite.
• 36120 is not a perfect square.
• Number of divisors: 64.
• Sum of divisors: 126720.

Common Divisors with Another Number?

Looking for the divisors that 36120 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 36120

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √36120 ≈ 190.05. If i divides 36120, then both i and 36120/i are divisors.

1. 1 divides 36120 (36120 ÷ 1 = 36120) → pair (1, 36120)
2. 2 divides 36120 (36120 ÷ 2 = 18060) → pair (2, 18060)
3. 3 divides 36120 (36120 ÷ 3 = 12040) → pair (3, 12040)
4. 4 divides 36120 (36120 ÷ 4 = 9030) → pair (4, 9030)
5. 5 divides 36120 (36120 ÷ 5 = 7224) → pair (5, 7224)
6. 6 divides 36120 (36120 ÷ 6 = 6020) → pair (6, 6020)
7. 7 divides 36120 (36120 ÷ 7 = 5160) → pair (7, 5160)
8. 8 divides 36120 (36120 ÷ 8 = 4515) → pair (8, 4515)
9. 10 divides 36120 (36120 ÷ 10 = 3612) → pair (10, 3612)
10. 12 divides 36120 (36120 ÷ 12 = 3010) → pair (12, 3010)
11. 14 divides 36120 (36120 ÷ 14 = 2580) → pair (14, 2580)
12. 15 divides 36120 (36120 ÷ 15 = 2408) → pair (15, 2408)
13. 20 divides 36120 (36120 ÷ 20 = 1806) → pair (20, 1806)
14. 21 divides 36120 (36120 ÷ 21 = 1720) → pair (21, 1720)
15. 24 divides 36120 (36120 ÷ 24 = 1505) → pair (24, 1505)
16. 28 divides 36120 (36120 ÷ 28 = 1290) → pair (28, 1290)
17. 30 divides 36120 (36120 ÷ 30 = 1204) → pair (30, 1204)
18. 35 divides 36120 (36120 ÷ 35 = 1032) → pair (35, 1032)
19. 40 divides 36120 (36120 ÷ 40 = 903) → pair (40, 903)
20. 42 divides 36120 (36120 ÷ 42 = 860) → pair (42, 860)
21. 43 divides 36120 (36120 ÷ 43 = 840) → pair (43, 840)
22. 56 divides 36120 (36120 ÷ 56 = 645) → pair (56, 645)
23. 60 divides 36120 (36120 ÷ 60 = 602) → pair (60, 602)
24. 70 divides 36120 (36120 ÷ 70 = 516) → pair (70, 516)
25. 84 divides 36120 (36120 ÷ 84 = 430) → pair (84, 430)
26. 86 divides 36120 (36120 ÷ 86 = 420) → pair (86, 420)
27. 105 divides 36120 (36120 ÷ 105 = 344) → pair (105, 344)
28. 120 divides 36120 (36120 ÷ 120 = 301) → pair (120, 301)
29. 129 divides 36120 (36120 ÷ 129 = 280) → pair (129, 280)
30. 140 divides 36120 (36120 ÷ 140 = 258) → pair (140, 258)
31. 168 divides 36120 (36120 ÷ 168 = 215) → pair (168, 215)
32. 172 divides 36120 (36120 ÷ 172 = 210) → pair (172, 210)
33. Collect all unique values: {1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 43, 56, 60, 70, 84, 86, 105, 120, 129, 140, 168, 172, 210, 215, 258, 280, 301, 344, 420, 430, 516, 602, 645, 840, 860, 903, 1032, 1204, 1290, 1505, 1720, 1806, 2408, 2580, 3010, 3612, 4515, 5160, 6020, 7224, 9030, 12040, 18060, 36120} — total 64 divisors.
34. Sum: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 10 + 12 + 14 + 15 + 20 + 21 + 24 + 28 + 30 + 35 + 40 + 42 + 43 + 56 + 60 + 70 + 84 + 86 + 105 + 120 + 129 + 140 + 168 + 172 + 210 + 215 + 258 + 280 + 301 + 344 + 420 + 430 + 516 + 602 + 645 + 840 + 860 + 903 + 1032 + 1204 + 1290 + 1505 + 1720 + 1806 + 2408 + 2580 + 3010 + 3612 + 4515 + 5160 + 6020 + 7224 + 9030 + 12040 + 18060 + 36120 = 126720.

Nearby Examples

Related Operations for 36120

• Multiples of a Number — "outward" complement of divisors
• 36120 Prime Factorization — decompose into prime building blocks
• Find GCF of 36120 and another number
• Find LCM of 36120 and another number
• Is 36120 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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