Divisors of 38400: All 60 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 38400

The number 38400 has 60 divisors:

1,  2,  3,  4,  5,  6,  8,  10,  12,  15,  16,  20,  24,  25,  30,  32,  40,  48,  50,  60,  64,  75,  80,  96,  100,  120,  128,  150,  160,  192,  200,  240,  256,  300,  320,  384,  400,  480,  512,  600,  640,  768,  800,  960,  1200,  1280,  1536,  1600,  1920,  2400,  2560,  3200,  3840,  4800,  6400,  7680,  9600,  12800,  19200,  38400

Divisor Pairs of 38400

Each pair multiplies to 38400:

Number of Divisors

The number 38400 has 60 divisors, written as τ(38400) = 60 in number theory.

Sum of Divisors

σ(38400) = 1 + 2 + 3 + 4 + 5 + 6 + 8 + 10 + 12 + 15 + 16 + 20 + 24 + 25 + 30 + 32 + 40 + 48 + 50 + 60 + 64 + 75 + 80 + 96 + 100 + 120 + 128 + 150 + 160 + 192 + 200 + 240 + 256 + 300 + 320 + 384 + 400 + 480 + 512 + 600 + 640 + 768 + 800 + 960 + 1200 + 1280 + 1536 + 1600 + 1920 + 2400 + 2560 + 3200 + 3840 + 4800 + 6400 + 7680 + 9600 + 12800 + 19200 + 38400 = 126852

Prime Factorization of 38400

See the full prime factorization calculator →

Properties of 38400

• 38400 is composite.
• 38400 is not a perfect square.
• Number of divisors: 60.
• Sum of divisors: 126852.

Common Divisors with Another Number?

Looking for the divisors that 38400 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 38400

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √38400 ≈ 195.96. If i divides 38400, then both i and 38400/i are divisors.

1. 1 divides 38400 (38400 ÷ 1 = 38400) → pair (1, 38400)
2. 2 divides 38400 (38400 ÷ 2 = 19200) → pair (2, 19200)
3. 3 divides 38400 (38400 ÷ 3 = 12800) → pair (3, 12800)
4. 4 divides 38400 (38400 ÷ 4 = 9600) → pair (4, 9600)
5. 5 divides 38400 (38400 ÷ 5 = 7680) → pair (5, 7680)
6. 6 divides 38400 (38400 ÷ 6 = 6400) → pair (6, 6400)
7. 8 divides 38400 (38400 ÷ 8 = 4800) → pair (8, 4800)
8. 10 divides 38400 (38400 ÷ 10 = 3840) → pair (10, 3840)
9. 12 divides 38400 (38400 ÷ 12 = 3200) → pair (12, 3200)
10. 15 divides 38400 (38400 ÷ 15 = 2560) → pair (15, 2560)
11. 16 divides 38400 (38400 ÷ 16 = 2400) → pair (16, 2400)
12. 20 divides 38400 (38400 ÷ 20 = 1920) → pair (20, 1920)
13. 24 divides 38400 (38400 ÷ 24 = 1600) → pair (24, 1600)
14. 25 divides 38400 (38400 ÷ 25 = 1536) → pair (25, 1536)
15. 30 divides 38400 (38400 ÷ 30 = 1280) → pair (30, 1280)
16. 32 divides 38400 (38400 ÷ 32 = 1200) → pair (32, 1200)
17. 40 divides 38400 (38400 ÷ 40 = 960) → pair (40, 960)
18. 48 divides 38400 (38400 ÷ 48 = 800) → pair (48, 800)
19. 50 divides 38400 (38400 ÷ 50 = 768) → pair (50, 768)
20. 60 divides 38400 (38400 ÷ 60 = 640) → pair (60, 640)
21. 64 divides 38400 (38400 ÷ 64 = 600) → pair (64, 600)
22. 75 divides 38400 (38400 ÷ 75 = 512) → pair (75, 512)
23. 80 divides 38400 (38400 ÷ 80 = 480) → pair (80, 480)
24. 96 divides 38400 (38400 ÷ 96 = 400) → pair (96, 400)
25. 100 divides 38400 (38400 ÷ 100 = 384) → pair (100, 384)
26. 120 divides 38400 (38400 ÷ 120 = 320) → pair (120, 320)
27. 128 divides 38400 (38400 ÷ 128 = 300) → pair (128, 300)
28. 150 divides 38400 (38400 ÷ 150 = 256) → pair (150, 256)
29. 160 divides 38400 (38400 ÷ 160 = 240) → pair (160, 240)
30. 192 divides 38400 (38400 ÷ 192 = 200) → pair (192, 200)
31. Collect all unique values: {1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 64, 75, 80, 96, 100, 120, 128, 150, 160, 192, 200, 240, 256, 300, 320, 384, 400, 480, 512, 600, 640, 768, 800, 960, 1200, 1280, 1536, 1600, 1920, 2400, 2560, 3200, 3840, 4800, 6400, 7680, 9600, 12800, 19200, 38400} — total 60 divisors.
32. Sum: 1 + 2 + 3 + 4 + 5 + 6 + 8 + 10 + 12 + 15 + 16 + 20 + 24 + 25 + 30 + 32 + 40 + 48 + 50 + 60 + 64 + 75 + 80 + 96 + 100 + 120 + 128 + 150 + 160 + 192 + 200 + 240 + 256 + 300 + 320 + 384 + 400 + 480 + 512 + 600 + 640 + 768 + 800 + 960 + 1200 + 1280 + 1536 + 1600 + 1920 + 2400 + 2560 + 3200 + 3840 + 4800 + 6400 + 7680 + 9600 + 12800 + 19200 + 38400 = 126852.

Nearby Examples

Related Operations for 38400

• Multiples of a Number — "outward" complement of divisors
• 38400 Prime Factorization — decompose into prime building blocks
• Find GCF of 38400 and another number
• Find LCM of 38400 and another number
• Is 38400 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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