Divisors of 48384: 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 48384

The number 48384 has 72 divisors:

1,  2,  3,  4,  6,  7,  8,  9,  12,  14,  16,  18,  21,  24,  27,  28,  32,  36,  42,  48,  54,  56,  63,  64,  72,  84,  96,  108,  112,  126,  128,  144,  168,  189,  192,  216,  224,  252,  256,  288,  336,  378,  384,  432,  448,  504,  576,  672,  756,  768,  864,  896,  1008,  1152,  1344,  1512,  1728,  1792,  2016,  2304,  2688,  3024,  3456,  4032,  5376,  6048,  6912,  8064,  12096,  16128,  24192,  48384

Divisor Pairs of 48384

Each pair multiplies to 48384:

Number of Divisors

The number 48384 has 72 divisors, written as τ(48384) = 72 in number theory.

Sum of Divisors

σ(48384) = 1 + 2 + 3 + 4 + 6 + 7 + 8 + 9 + 12 + 14 + 16 + 18 + 21 + 24 + 27 + 28 + 32 + 36 + 42 + 48 + 54 + 56 + 63 + 64 + 72 + 84 + 96 + 108 + 112 + 126 + 128 + 144 + 168 + 189 + 192 + 216 + 224 + 252 + 256 + 288 + 336 + 378 + 384 + 432 + 448 + 504 + 576 + 672 + 756 + 768 + 864 + 896 + 1008 + 1152 + 1344 + 1512 + 1728 + 1792 + 2016 + 2304 + 2688 + 3024 + 3456 + 4032 + 5376 + 6048 + 6912 + 8064 + 12096 + 16128 + 24192 + 48384 = 163520

Prime Factorization of 48384

See the full prime factorization calculator →

Properties of 48384

• 48384 is composite.
• 48384 is not a perfect square.
• Number of divisors: 72.
• Sum of divisors: 163520.

Common Divisors with Another Number?

Looking for the divisors that 48384 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 48384

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √48384 ≈ 219.96. If i divides 48384, then both i and 48384/i are divisors.

1. 1 divides 48384 (48384 ÷ 1 = 48384) → pair (1, 48384)
2. 2 divides 48384 (48384 ÷ 2 = 24192) → pair (2, 24192)
3. 3 divides 48384 (48384 ÷ 3 = 16128) → pair (3, 16128)
4. 4 divides 48384 (48384 ÷ 4 = 12096) → pair (4, 12096)
5. 6 divides 48384 (48384 ÷ 6 = 8064) → pair (6, 8064)
6. 7 divides 48384 (48384 ÷ 7 = 6912) → pair (7, 6912)
7. 8 divides 48384 (48384 ÷ 8 = 6048) → pair (8, 6048)
8. 9 divides 48384 (48384 ÷ 9 = 5376) → pair (9, 5376)
9. 12 divides 48384 (48384 ÷ 12 = 4032) → pair (12, 4032)
10. 14 divides 48384 (48384 ÷ 14 = 3456) → pair (14, 3456)
11. 16 divides 48384 (48384 ÷ 16 = 3024) → pair (16, 3024)
12. 18 divides 48384 (48384 ÷ 18 = 2688) → pair (18, 2688)
13. 21 divides 48384 (48384 ÷ 21 = 2304) → pair (21, 2304)
14. 24 divides 48384 (48384 ÷ 24 = 2016) → pair (24, 2016)
15. 27 divides 48384 (48384 ÷ 27 = 1792) → pair (27, 1792)
16. 28 divides 48384 (48384 ÷ 28 = 1728) → pair (28, 1728)
17. 32 divides 48384 (48384 ÷ 32 = 1512) → pair (32, 1512)
18. 36 divides 48384 (48384 ÷ 36 = 1344) → pair (36, 1344)
19. 42 divides 48384 (48384 ÷ 42 = 1152) → pair (42, 1152)
20. 48 divides 48384 (48384 ÷ 48 = 1008) → pair (48, 1008)
21. 54 divides 48384 (48384 ÷ 54 = 896) → pair (54, 896)
22. 56 divides 48384 (48384 ÷ 56 = 864) → pair (56, 864)
23. 63 divides 48384 (48384 ÷ 63 = 768) → pair (63, 768)
24. 64 divides 48384 (48384 ÷ 64 = 756) → pair (64, 756)
25. 72 divides 48384 (48384 ÷ 72 = 672) → pair (72, 672)
26. 84 divides 48384 (48384 ÷ 84 = 576) → pair (84, 576)
27. 96 divides 48384 (48384 ÷ 96 = 504) → pair (96, 504)
28. 108 divides 48384 (48384 ÷ 108 = 448) → pair (108, 448)
29. 112 divides 48384 (48384 ÷ 112 = 432) → pair (112, 432)
30. 126 divides 48384 (48384 ÷ 126 = 384) → pair (126, 384)
31. 128 divides 48384 (48384 ÷ 128 = 378) → pair (128, 378)
32. 144 divides 48384 (48384 ÷ 144 = 336) → pair (144, 336)
33. 168 divides 48384 (48384 ÷ 168 = 288) → pair (168, 288)
34. 189 divides 48384 (48384 ÷ 189 = 256) → pair (189, 256)
35. 192 divides 48384 (48384 ÷ 192 = 252) → pair (192, 252)
36. 216 divides 48384 (48384 ÷ 216 = 224) → pair (216, 224)
37. Collect all unique values: {1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 27, 28, 32, 36, 42, 48, 54, 56, 63, 64, 72, 84, 96, 108, 112, 126, 128, 144, 168, 189, 192, 216, 224, 252, 256, 288, 336, 378, 384, 432, 448, 504, 576, 672, 756, 768, 864, 896, 1008, 1152, 1344, 1512, 1728, 1792, 2016, 2304, 2688, 3024, 3456, 4032, 5376, 6048, 6912, 8064, 12096, 16128, 24192, 48384} — total 72 divisors.
38. Sum: 1 + 2 + 3 + 4 + 6 + 7 + 8 + 9 + 12 + 14 + 16 + 18 + 21 + 24 + 27 + 28 + 32 + 36 + 42 + 48 + 54 + 56 + 63 + 64 + 72 + 84 + 96 + 108 + 112 + 126 + 128 + 144 + 168 + 189 + 192 + 216 + 224 + 252 + 256 + 288 + 336 + 378 + 384 + 432 + 448 + 504 + 576 + 672 + 756 + 768 + 864 + 896 + 1008 + 1152 + 1344 + 1512 + 1728 + 1792 + 2016 + 2304 + 2688 + 3024 + 3456 + 4032 + 5376 + 6048 + 6912 + 8064 + 12096 + 16128 + 24192 + 48384 = 163520.

Nearby Examples

Related Operations for 48384

• Multiples of a Number — "outward" complement of divisors
• 48384 Prime Factorization — decompose into prime building blocks
• Find GCF of 48384 and another number
• Find LCM of 48384 and another number
• Is 48384 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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