Divisors of 40800: 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 40800

The number 40800 has 72 divisors:

1,  2,  3,  4,  5,  6,  8,  10,  12,  15,  16,  17,  20,  24,  25,  30,  32,  34,  40,  48,  50,  51,  60,  68,  75,  80,  85,  96,  100,  102,  120,  136,  150,  160,  170,  200,  204,  240,  255,  272,  300,  340,  400,  408,  425,  480,  510,  544,  600,  680,  800,  816,  850,  1020,  1200,  1275,  1360,  1632,  1700,  2040,  2400,  2550,  2720,  3400,  4080,  5100,  6800,  8160,  10200,  13600,  20400,  40800

Divisor Pairs of 40800

Each pair multiplies to 40800:

Number of Divisors

The number 40800 has 72 divisors, written as τ(40800) = 72 in number theory.

Sum of Divisors

σ(40800) = 1 + 2 + 3 + 4 + 5 + 6 + 8 + 10 + 12 + 15 + 16 + 17 + 20 + 24 + 25 + 30 + 32 + 34 + 40 + 48 + 50 + 51 + 60 + 68 + 75 + 80 + 85 + 96 + 100 + 102 + 120 + 136 + 150 + 160 + 170 + 200 + 204 + 240 + 255 + 272 + 300 + 340 + 400 + 408 + 425 + 480 + 510 + 544 + 600 + 680 + 800 + 816 + 850 + 1020 + 1200 + 1275 + 1360 + 1632 + 1700 + 2040 + 2400 + 2550 + 2720 + 3400 + 4080 + 5100 + 6800 + 8160 + 10200 + 13600 + 20400 + 40800 = 140616

Prime Factorization of 40800

See the full prime factorization calculator →

Properties of 40800

• 40800 is composite.
• 40800 is not a perfect square.
• Number of divisors: 72.
• Sum of divisors: 140616.

Common Divisors with Another Number?

Looking for the divisors that 40800 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 40800

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √40800 ≈ 201.99. If i divides 40800, then both i and 40800/i are divisors.

1. 1 divides 40800 (40800 ÷ 1 = 40800) → pair (1, 40800)
2. 2 divides 40800 (40800 ÷ 2 = 20400) → pair (2, 20400)
3. 3 divides 40800 (40800 ÷ 3 = 13600) → pair (3, 13600)
4. 4 divides 40800 (40800 ÷ 4 = 10200) → pair (4, 10200)
5. 5 divides 40800 (40800 ÷ 5 = 8160) → pair (5, 8160)
6. 6 divides 40800 (40800 ÷ 6 = 6800) → pair (6, 6800)
7. 8 divides 40800 (40800 ÷ 8 = 5100) → pair (8, 5100)
8. 10 divides 40800 (40800 ÷ 10 = 4080) → pair (10, 4080)
9. 12 divides 40800 (40800 ÷ 12 = 3400) → pair (12, 3400)
10. 15 divides 40800 (40800 ÷ 15 = 2720) → pair (15, 2720)
11. 16 divides 40800 (40800 ÷ 16 = 2550) → pair (16, 2550)
12. 17 divides 40800 (40800 ÷ 17 = 2400) → pair (17, 2400)
13. 20 divides 40800 (40800 ÷ 20 = 2040) → pair (20, 2040)
14. 24 divides 40800 (40800 ÷ 24 = 1700) → pair (24, 1700)
15. 25 divides 40800 (40800 ÷ 25 = 1632) → pair (25, 1632)
16. 30 divides 40800 (40800 ÷ 30 = 1360) → pair (30, 1360)
17. 32 divides 40800 (40800 ÷ 32 = 1275) → pair (32, 1275)
18. 34 divides 40800 (40800 ÷ 34 = 1200) → pair (34, 1200)
19. 40 divides 40800 (40800 ÷ 40 = 1020) → pair (40, 1020)
20. 48 divides 40800 (40800 ÷ 48 = 850) → pair (48, 850)
21. 50 divides 40800 (40800 ÷ 50 = 816) → pair (50, 816)
22. 51 divides 40800 (40800 ÷ 51 = 800) → pair (51, 800)
23. 60 divides 40800 (40800 ÷ 60 = 680) → pair (60, 680)
24. 68 divides 40800 (40800 ÷ 68 = 600) → pair (68, 600)
25. 75 divides 40800 (40800 ÷ 75 = 544) → pair (75, 544)
26. 80 divides 40800 (40800 ÷ 80 = 510) → pair (80, 510)
27. 85 divides 40800 (40800 ÷ 85 = 480) → pair (85, 480)
28. 96 divides 40800 (40800 ÷ 96 = 425) → pair (96, 425)
29. 100 divides 40800 (40800 ÷ 100 = 408) → pair (100, 408)
30. 102 divides 40800 (40800 ÷ 102 = 400) → pair (102, 400)
31. 120 divides 40800 (40800 ÷ 120 = 340) → pair (120, 340)
32. 136 divides 40800 (40800 ÷ 136 = 300) → pair (136, 300)
33. 150 divides 40800 (40800 ÷ 150 = 272) → pair (150, 272)
34. 160 divides 40800 (40800 ÷ 160 = 255) → pair (160, 255)
35. 170 divides 40800 (40800 ÷ 170 = 240) → pair (170, 240)
36. 200 divides 40800 (40800 ÷ 200 = 204) → pair (200, 204)
37. Collect all unique values: {1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 17, 20, 24, 25, 30, 32, 34, 40, 48, 50, 51, 60, 68, 75, 80, 85, 96, 100, 102, 120, 136, 150, 160, 170, 200, 204, 240, 255, 272, 300, 340, 400, 408, 425, 480, 510, 544, 600, 680, 800, 816, 850, 1020, 1200, 1275, 1360, 1632, 1700, 2040, 2400, 2550, 2720, 3400, 4080, 5100, 6800, 8160, 10200, 13600, 20400, 40800} — total 72 divisors.
38. Sum: 1 + 2 + 3 + 4 + 5 + 6 + 8 + 10 + 12 + 15 + 16 + 17 + 20 + 24 + 25 + 30 + 32 + 34 + 40 + 48 + 50 + 51 + 60 + 68 + 75 + 80 + 85 + 96 + 100 + 102 + 120 + 136 + 150 + 160 + 170 + 200 + 204 + 240 + 255 + 272 + 300 + 340 + 400 + 408 + 425 + 480 + 510 + 544 + 600 + 680 + 800 + 816 + 850 + 1020 + 1200 + 1275 + 1360 + 1632 + 1700 + 2040 + 2400 + 2550 + 2720 + 3400 + 4080 + 5100 + 6800 + 8160 + 10200 + 13600 + 20400 + 40800 = 140616.

Nearby Examples

Related Operations for 40800

• Multiples of a Number — "outward" complement of divisors
• 40800 Prime Factorization — decompose into prime building blocks
• Find GCF of 40800 and another number
• Find LCM of 40800 and another number
• Is 40800 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: