Divisors of 25200: All 90 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 25200

The number 25200 has 90 divisors:

1,  2,  3,  4,  5,  6,  7,  8,  9,  10,  12,  14,  15,  16,  18,  20,  21,  24,  25,  28,  30,  35,  36,  40,  42,  45,  48,  50,  56,  60,  63,  70,  72,  75,  80,  84,  90,  100,  105,  112,  120,  126,  140,  144,  150,  168,  175,  180,  200,  210,  225,  240,  252,  280,  300,  315,  336,  350,  360,  400,  420,  450,  504,  525,  560,  600,  630,  700,  720,  840,  900,  1008,  1050,  1200,  1260,  1400,  1575,  1680,  1800,  2100,  2520,  2800,  3150,  3600,  4200,  5040,  6300,  8400,  12600,  25200

Divisor Pairs of 25200

Each pair multiplies to 25200:

Number of Divisors

The number 25200 has 90 divisors, written as τ(25200) = 90 in number theory.

Sum of Divisors

σ(25200) = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 12 + 14 + 15 + 16 + 18 + 20 + 21 + 24 + 25 + 28 + 30 + 35 + 36 + 40 + 42 + 45 + 48 + 50 + 56 + 60 + 63 + 70 + 72 + 75 + 80 + 84 + 90 + 100 + 105 + 112 + 120 + 126 + 140 + 144 + 150 + 168 + 175 + 180 + 200 + 210 + 225 + 240 + 252 + 280 + 300 + 315 + 336 + 350 + 360 + 400 + 420 + 450 + 504 + 525 + 560 + 600 + 630 + 700 + 720 + 840 + 900 + 1008 + 1050 + 1200 + 1260 + 1400 + 1575 + 1680 + 1800 + 2100 + 2520 + 2800 + 3150 + 3600 + 4200 + 5040 + 6300 + 8400 + 12600 + 25200 = 99944

Prime Factorization of 25200

See the full prime factorization calculator →

Properties of 25200

• 25200 is composite.
• 25200 is not a perfect square.
• Number of divisors: 90.
• Sum of divisors: 99944.

Common Divisors with Another Number?

Looking for the divisors that 25200 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 25200

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √25200 ≈ 158.75. If i divides 25200, then both i and 25200/i are divisors.

1. 1 divides 25200 (25200 ÷ 1 = 25200) → pair (1, 25200)
2. 2 divides 25200 (25200 ÷ 2 = 12600) → pair (2, 12600)
3. 3 divides 25200 (25200 ÷ 3 = 8400) → pair (3, 8400)
4. 4 divides 25200 (25200 ÷ 4 = 6300) → pair (4, 6300)
5. 5 divides 25200 (25200 ÷ 5 = 5040) → pair (5, 5040)
6. 6 divides 25200 (25200 ÷ 6 = 4200) → pair (6, 4200)
7. 7 divides 25200 (25200 ÷ 7 = 3600) → pair (7, 3600)
8. 8 divides 25200 (25200 ÷ 8 = 3150) → pair (8, 3150)
9. 9 divides 25200 (25200 ÷ 9 = 2800) → pair (9, 2800)
10. 10 divides 25200 (25200 ÷ 10 = 2520) → pair (10, 2520)
11. 12 divides 25200 (25200 ÷ 12 = 2100) → pair (12, 2100)
12. 14 divides 25200 (25200 ÷ 14 = 1800) → pair (14, 1800)
13. 15 divides 25200 (25200 ÷ 15 = 1680) → pair (15, 1680)
14. 16 divides 25200 (25200 ÷ 16 = 1575) → pair (16, 1575)
15. 18 divides 25200 (25200 ÷ 18 = 1400) → pair (18, 1400)
16. 20 divides 25200 (25200 ÷ 20 = 1260) → pair (20, 1260)
17. 21 divides 25200 (25200 ÷ 21 = 1200) → pair (21, 1200)
18. 24 divides 25200 (25200 ÷ 24 = 1050) → pair (24, 1050)
19. 25 divides 25200 (25200 ÷ 25 = 1008) → pair (25, 1008)
20. 28 divides 25200 (25200 ÷ 28 = 900) → pair (28, 900)
21. 30 divides 25200 (25200 ÷ 30 = 840) → pair (30, 840)
22. 35 divides 25200 (25200 ÷ 35 = 720) → pair (35, 720)
23. 36 divides 25200 (25200 ÷ 36 = 700) → pair (36, 700)
24. 40 divides 25200 (25200 ÷ 40 = 630) → pair (40, 630)
25. 42 divides 25200 (25200 ÷ 42 = 600) → pair (42, 600)
26. 45 divides 25200 (25200 ÷ 45 = 560) → pair (45, 560)
27. 48 divides 25200 (25200 ÷ 48 = 525) → pair (48, 525)
28. 50 divides 25200 (25200 ÷ 50 = 504) → pair (50, 504)
29. 56 divides 25200 (25200 ÷ 56 = 450) → pair (56, 450)
30. 60 divides 25200 (25200 ÷ 60 = 420) → pair (60, 420)
31. 63 divides 25200 (25200 ÷ 63 = 400) → pair (63, 400)
32. 70 divides 25200 (25200 ÷ 70 = 360) → pair (70, 360)
33. 72 divides 25200 (25200 ÷ 72 = 350) → pair (72, 350)
34. 75 divides 25200 (25200 ÷ 75 = 336) → pair (75, 336)
35. 80 divides 25200 (25200 ÷ 80 = 315) → pair (80, 315)
36. 84 divides 25200 (25200 ÷ 84 = 300) → pair (84, 300)
37. 90 divides 25200 (25200 ÷ 90 = 280) → pair (90, 280)
38. 100 divides 25200 (25200 ÷ 100 = 252) → pair (100, 252)
39. 105 divides 25200 (25200 ÷ 105 = 240) → pair (105, 240)
40. 112 divides 25200 (25200 ÷ 112 = 225) → pair (112, 225)
41. 120 divides 25200 (25200 ÷ 120 = 210) → pair (120, 210)
42. 126 divides 25200 (25200 ÷ 126 = 200) → pair (126, 200)
43. 140 divides 25200 (25200 ÷ 140 = 180) → pair (140, 180)
44. 144 divides 25200 (25200 ÷ 144 = 175) → pair (144, 175)
45. 150 divides 25200 (25200 ÷ 150 = 168) → pair (150, 168)
46. Collect all unique values: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 25, 28, 30, 35, 36, 40, 42, 45, 48, 50, 56, 60, 63, 70, 72, 75, 80, 84, 90, 100, 105, 112, 120, 126, 140, 144, 150, 168, 175, 180, 200, 210, 225, 240, 252, 280, 300, 315, 336, 350, 360, 400, 420, 450, 504, 525, 560, 600, 630, 700, 720, 840, 900, 1008, 1050, 1200, 1260, 1400, 1575, 1680, 1800, 2100, 2520, 2800, 3150, 3600, 4200, 5040, 6300, 8400, 12600, 25200} — total 90 divisors.
47. Sum: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 12 + 14 + 15 + 16 + 18 + 20 + 21 + 24 + 25 + 28 + 30 + 35 + 36 + 40 + 42 + 45 + 48 + 50 + 56 + 60 + 63 + 70 + 72 + 75 + 80 + 84 + 90 + 100 + 105 + 112 + 120 + 126 + 140 + 144 + 150 + 168 + 175 + 180 + 200 + 210 + 225 + 240 + 252 + 280 + 300 + 315 + 336 + 350 + 360 + 400 + 420 + 450 + 504 + 525 + 560 + 600 + 630 + 700 + 720 + 840 + 900 + 1008 + 1050 + 1200 + 1260 + 1400 + 1575 + 1680 + 1800 + 2100 + 2520 + 2800 + 3150 + 3600 + 4200 + 5040 + 6300 + 8400 + 12600 + 25200 = 99944.

Nearby Examples

Related Operations for 25200

• Multiples of a Number — "outward" complement of divisors
• 25200 Prime Factorization — decompose into prime building blocks
• Find GCF of 25200 and another number
• Find LCM of 25200 and another number
• Is 25200 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: