Divisors of 48960: All 84 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 48960

The number 48960 has 84 divisors:

1,  2,  3,  4,  5,  6,  8,  9,  10,  12,  15,  16,  17,  18,  20,  24,  30,  32,  34,  36,  40,  45,  48,  51,  60,  64,  68,  72,  80,  85,  90,  96,  102,  120,  136,  144,  153,  160,  170,  180,  192,  204,  240,  255,  272,  288,  306,  320,  340,  360,  408,  480,  510,  544,  576,  612,  680,  720,  765,  816,  960,  1020,  1088,  1224,  1360,  1440,  1530,  1632,  2040,  2448,  2720,  2880,  3060,  3264,  4080,  4896,  5440,  6120,  8160,  9792,  12240,  16320,  24480,  48960

Divisor Pairs of 48960

Each pair multiplies to 48960:

Number of Divisors

The number 48960 has 84 divisors, written as τ(48960) = 84 in number theory.

Sum of Divisors

σ(48960) = 1 + 2 + 3 + 4 + 5 + 6 + 8 + 9 + 10 + 12 + 15 + 16 + 17 + 18 + 20 + 24 + 30 + 32 + 34 + 36 + 40 + 45 + 48 + 51 + 60 + 64 + 68 + 72 + 80 + 85 + 90 + 96 + 102 + 120 + 136 + 144 + 153 + 160 + 170 + 180 + 192 + 204 + 240 + 255 + 272 + 288 + 306 + 320 + 340 + 360 + 408 + 480 + 510 + 544 + 576 + 612 + 680 + 720 + 765 + 816 + 960 + 1020 + 1088 + 1224 + 1360 + 1440 + 1530 + 1632 + 2040 + 2448 + 2720 + 2880 + 3060 + 3264 + 4080 + 4896 + 5440 + 6120 + 8160 + 9792 + 12240 + 16320 + 24480 + 48960 = 178308

Prime Factorization of 48960

See the full prime factorization calculator →

Properties of 48960

• 48960 is composite.
• 48960 is not a perfect square.
• Number of divisors: 84.
• Sum of divisors: 178308.

Common Divisors with Another Number?

Looking for the divisors that 48960 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 48960

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √48960 ≈ 221.27. If i divides 48960, then both i and 48960/i are divisors.

1. 1 divides 48960 (48960 ÷ 1 = 48960) → pair (1, 48960)
2. 2 divides 48960 (48960 ÷ 2 = 24480) → pair (2, 24480)
3. 3 divides 48960 (48960 ÷ 3 = 16320) → pair (3, 16320)
4. 4 divides 48960 (48960 ÷ 4 = 12240) → pair (4, 12240)
5. 5 divides 48960 (48960 ÷ 5 = 9792) → pair (5, 9792)
6. 6 divides 48960 (48960 ÷ 6 = 8160) → pair (6, 8160)
7. 8 divides 48960 (48960 ÷ 8 = 6120) → pair (8, 6120)
8. 9 divides 48960 (48960 ÷ 9 = 5440) → pair (9, 5440)
9. 10 divides 48960 (48960 ÷ 10 = 4896) → pair (10, 4896)
10. 12 divides 48960 (48960 ÷ 12 = 4080) → pair (12, 4080)
11. 15 divides 48960 (48960 ÷ 15 = 3264) → pair (15, 3264)
12. 16 divides 48960 (48960 ÷ 16 = 3060) → pair (16, 3060)
13. 17 divides 48960 (48960 ÷ 17 = 2880) → pair (17, 2880)
14. 18 divides 48960 (48960 ÷ 18 = 2720) → pair (18, 2720)
15. 20 divides 48960 (48960 ÷ 20 = 2448) → pair (20, 2448)
16. 24 divides 48960 (48960 ÷ 24 = 2040) → pair (24, 2040)
17. 30 divides 48960 (48960 ÷ 30 = 1632) → pair (30, 1632)
18. 32 divides 48960 (48960 ÷ 32 = 1530) → pair (32, 1530)
19. 34 divides 48960 (48960 ÷ 34 = 1440) → pair (34, 1440)
20. 36 divides 48960 (48960 ÷ 36 = 1360) → pair (36, 1360)
21. 40 divides 48960 (48960 ÷ 40 = 1224) → pair (40, 1224)
22. 45 divides 48960 (48960 ÷ 45 = 1088) → pair (45, 1088)
23. 48 divides 48960 (48960 ÷ 48 = 1020) → pair (48, 1020)
24. 51 divides 48960 (48960 ÷ 51 = 960) → pair (51, 960)
25. 60 divides 48960 (48960 ÷ 60 = 816) → pair (60, 816)
26. 64 divides 48960 (48960 ÷ 64 = 765) → pair (64, 765)
27. 68 divides 48960 (48960 ÷ 68 = 720) → pair (68, 720)
28. 72 divides 48960 (48960 ÷ 72 = 680) → pair (72, 680)
29. 80 divides 48960 (48960 ÷ 80 = 612) → pair (80, 612)
30. 85 divides 48960 (48960 ÷ 85 = 576) → pair (85, 576)
31. 90 divides 48960 (48960 ÷ 90 = 544) → pair (90, 544)
32. 96 divides 48960 (48960 ÷ 96 = 510) → pair (96, 510)
33. 102 divides 48960 (48960 ÷ 102 = 480) → pair (102, 480)
34. 120 divides 48960 (48960 ÷ 120 = 408) → pair (120, 408)
35. 136 divides 48960 (48960 ÷ 136 = 360) → pair (136, 360)
36. 144 divides 48960 (48960 ÷ 144 = 340) → pair (144, 340)
37. 153 divides 48960 (48960 ÷ 153 = 320) → pair (153, 320)
38. 160 divides 48960 (48960 ÷ 160 = 306) → pair (160, 306)
39. 170 divides 48960 (48960 ÷ 170 = 288) → pair (170, 288)
40. 180 divides 48960 (48960 ÷ 180 = 272) → pair (180, 272)
41. 192 divides 48960 (48960 ÷ 192 = 255) → pair (192, 255)
42. 204 divides 48960 (48960 ÷ 204 = 240) → pair (204, 240)
43. Collect all unique values: {1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 17, 18, 20, 24, 30, 32, 34, 36, 40, 45, 48, 51, 60, 64, 68, 72, 80, 85, 90, 96, 102, 120, 136, 144, 153, 160, 170, 180, 192, 204, 240, 255, 272, 288, 306, 320, 340, 360, 408, 480, 510, 544, 576, 612, 680, 720, 765, 816, 960, 1020, 1088, 1224, 1360, 1440, 1530, 1632, 2040, 2448, 2720, 2880, 3060, 3264, 4080, 4896, 5440, 6120, 8160, 9792, 12240, 16320, 24480, 48960} — total 84 divisors.
44. Sum: 1 + 2 + 3 + 4 + 5 + 6 + 8 + 9 + 10 + 12 + 15 + 16 + 17 + 18 + 20 + 24 + 30 + 32 + 34 + 36 + 40 + 45 + 48 + 51 + 60 + 64 + 68 + 72 + 80 + 85 + 90 + 96 + 102 + 120 + 136 + 144 + 153 + 160 + 170 + 180 + 192 + 204 + 240 + 255 + 272 + 288 + 306 + 320 + 340 + 360 + 408 + 480 + 510 + 544 + 576 + 612 + 680 + 720 + 765 + 816 + 960 + 1020 + 1088 + 1224 + 1360 + 1440 + 1530 + 1632 + 2040 + 2448 + 2720 + 2880 + 3060 + 3264 + 4080 + 4896 + 5440 + 6120 + 8160 + 9792 + 12240 + 16320 + 24480 + 48960 = 178308.

Nearby Examples

Related Operations for 48960

• Multiples of a Number — "outward" complement of divisors
• 48960 Prime Factorization — decompose into prime building blocks
• Find GCF of 48960 and another number
• Find LCM of 48960 and another number
• Is 48960 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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