Divisors of 14400: All 63 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 14400

The number 14400 has 63 divisors:

1,  2,  3,  4,  5,  6,  8,  9,  10,  12,  15,  16,  18,  20,  24,  25,  30,  32,  36,  40,  45,  48,  50,  60,  64,  72,  75,  80,  90,  96,  100,  120,  144,  150,  160,  180,  192,  200,  225,  240,  288,  300,  320,  360,  400,  450,  480,  576,  600,  720,  800,  900,  960,  1200,  1440,  1600,  1800,  2400,  2880,  3600,  4800,  7200,  14400

Divisor Pairs of 14400

Each pair multiplies to 14400:

Note: the last pair has identical factors (120 × 120) because 14400 is a perfect square.

Number of Divisors

The number 14400 has 63 divisors, written as τ(14400) = 63 in number theory.

⚡ Notice: 14400 has an odd number of divisors — this means 14400 is a perfect square (√14400 = 120).

Sum of Divisors

σ(14400) = 1 + 2 + 3 + 4 + 5 + 6 + 8 + 9 + 10 + 12 + 15 + 16 + 18 + 20 + 24 + 25 + 30 + 32 + 36 + 40 + 45 + 48 + 50 + 60 + 64 + 72 + 75 + 80 + 90 + 96 + 100 + 120 + 144 + 150 + 160 + 180 + 192 + 200 + 225 + 240 + 288 + 300 + 320 + 360 + 400 + 450 + 480 + 576 + 600 + 720 + 800 + 900 + 960 + 1200 + 1440 + 1600 + 1800 + 2400 + 2880 + 3600 + 4800 + 7200 + 14400 = 51181

Prime Factorization of 14400

See the full prime factorization calculator →

Properties of 14400

• 14400 is composite.
• 14400 is a perfect square (√14400 = 120).
• Number of divisors: 63.
• Sum of divisors: 51181.

Common Divisors with Another Number?

Looking for the divisors that 14400 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 14400

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √14400 ≈ 120.00. If i divides 14400, then both i and 14400/i are divisors.

1. 1 divides 14400 (14400 ÷ 1 = 14400) → pair (1, 14400)
2. 2 divides 14400 (14400 ÷ 2 = 7200) → pair (2, 7200)
3. 3 divides 14400 (14400 ÷ 3 = 4800) → pair (3, 4800)
4. 4 divides 14400 (14400 ÷ 4 = 3600) → pair (4, 3600)
5. 5 divides 14400 (14400 ÷ 5 = 2880) → pair (5, 2880)
6. 6 divides 14400 (14400 ÷ 6 = 2400) → pair (6, 2400)
7. 8 divides 14400 (14400 ÷ 8 = 1800) → pair (8, 1800)
8. 9 divides 14400 (14400 ÷ 9 = 1600) → pair (9, 1600)
9. 10 divides 14400 (14400 ÷ 10 = 1440) → pair (10, 1440)
10. 12 divides 14400 (14400 ÷ 12 = 1200) → pair (12, 1200)
11. 15 divides 14400 (14400 ÷ 15 = 960) → pair (15, 960)
12. 16 divides 14400 (14400 ÷ 16 = 900) → pair (16, 900)
13. 18 divides 14400 (14400 ÷ 18 = 800) → pair (18, 800)
14. 20 divides 14400 (14400 ÷ 20 = 720) → pair (20, 720)
15. 24 divides 14400 (14400 ÷ 24 = 600) → pair (24, 600)
16. 25 divides 14400 (14400 ÷ 25 = 576) → pair (25, 576)
17. 30 divides 14400 (14400 ÷ 30 = 480) → pair (30, 480)
18. 32 divides 14400 (14400 ÷ 32 = 450) → pair (32, 450)
19. 36 divides 14400 (14400 ÷ 36 = 400) → pair (36, 400)
20. 40 divides 14400 (14400 ÷ 40 = 360) → pair (40, 360)
21. 45 divides 14400 (14400 ÷ 45 = 320) → pair (45, 320)
22. 48 divides 14400 (14400 ÷ 48 = 300) → pair (48, 300)
23. 50 divides 14400 (14400 ÷ 50 = 288) → pair (50, 288)
24. 60 divides 14400 (14400 ÷ 60 = 240) → pair (60, 240)
25. 64 divides 14400 (14400 ÷ 64 = 225) → pair (64, 225)
26. 72 divides 14400 (14400 ÷ 72 = 200) → pair (72, 200)
27. 75 divides 14400 (14400 ÷ 75 = 192) → pair (75, 192)
28. 80 divides 14400 (14400 ÷ 80 = 180) → pair (80, 180)
29. 90 divides 14400 (14400 ÷ 90 = 160) → pair (90, 160)
30. 96 divides 14400 (14400 ÷ 96 = 150) → pair (96, 150)
31. 100 divides 14400 (14400 ÷ 100 = 144) → pair (100, 144)
32. 120 divides 14400 (14400 ÷ 120 = 120) → pair (120, 120)
33. Collect all unique values: {1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 32, 36, 40, 45, 48, 50, 60, 64, 72, 75, 80, 90, 96, 100, 120, 144, 150, 160, 180, 192, 200, 225, 240, 288, 300, 320, 360, 400, 450, 480, 576, 600, 720, 800, 900, 960, 1200, 1440, 1600, 1800, 2400, 2880, 3600, 4800, 7200, 14400} — total 63 divisors.
34. Sum: 1 + 2 + 3 + 4 + 5 + 6 + 8 + 9 + 10 + 12 + 15 + 16 + 18 + 20 + 24 + 25 + 30 + 32 + 36 + 40 + 45 + 48 + 50 + 60 + 64 + 72 + 75 + 80 + 90 + 96 + 100 + 120 + 144 + 150 + 160 + 180 + 192 + 200 + 225 + 240 + 288 + 300 + 320 + 360 + 400 + 450 + 480 + 576 + 600 + 720 + 800 + 900 + 960 + 1200 + 1440 + 1600 + 1800 + 2400 + 2880 + 3600 + 4800 + 7200 + 14400 = 51181.

Nearby Examples

Related Operations for 14400

• Multiples of a Number — "outward" complement of divisors
• 14400 Prime Factorization — decompose into prime building blocks
• Find GCF of 14400 and another number
• Find LCM of 14400 and another number
• Is 14400 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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