Divisors of 49920: 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 49920

The number 49920 has 72 divisors:

1,  2,  3,  4,  5,  6,  8,  10,  12,  13,  15,  16,  20,  24,  26,  30,  32,  39,  40,  48,  52,  60,  64,  65,  78,  80,  96,  104,  120,  128,  130,  156,  160,  192,  195,  208,  240,  256,  260,  312,  320,  384,  390,  416,  480,  520,  624,  640,  768,  780,  832,  960,  1040,  1248,  1280,  1560,  1664,  1920,  2080,  2496,  3120,  3328,  3840,  4160,  4992,  6240,  8320,  9984,  12480,  16640,  24960,  49920

Divisor Pairs of 49920

Each pair multiplies to 49920:

Number of Divisors

The number 49920 has 72 divisors, written as τ(49920) = 72 in number theory.

Sum of Divisors

σ(49920) = 1 + 2 + 3 + 4 + 5 + 6 + 8 + 10 + 12 + 13 + 15 + 16 + 20 + 24 + 26 + 30 + 32 + 39 + 40 + 48 + 52 + 60 + 64 + 65 + 78 + 80 + 96 + 104 + 120 + 128 + 130 + 156 + 160 + 192 + 195 + 208 + 240 + 256 + 260 + 312 + 320 + 384 + 390 + 416 + 480 + 520 + 624 + 640 + 768 + 780 + 832 + 960 + 1040 + 1248 + 1280 + 1560 + 1664 + 1920 + 2080 + 2496 + 3120 + 3328 + 3840 + 4160 + 4992 + 6240 + 8320 + 9984 + 12480 + 16640 + 24960 + 49920 = 171696

Prime Factorization of 49920

See the full prime factorization calculator →

Properties of 49920

• 49920 is composite.
• 49920 is not a perfect square.
• Number of divisors: 72.
• Sum of divisors: 171696.

Common Divisors with Another Number?

Looking for the divisors that 49920 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 49920

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √49920 ≈ 223.43. If i divides 49920, then both i and 49920/i are divisors.

1. 1 divides 49920 (49920 ÷ 1 = 49920) → pair (1, 49920)
2. 2 divides 49920 (49920 ÷ 2 = 24960) → pair (2, 24960)
3. 3 divides 49920 (49920 ÷ 3 = 16640) → pair (3, 16640)
4. 4 divides 49920 (49920 ÷ 4 = 12480) → pair (4, 12480)
5. 5 divides 49920 (49920 ÷ 5 = 9984) → pair (5, 9984)
6. 6 divides 49920 (49920 ÷ 6 = 8320) → pair (6, 8320)
7. 8 divides 49920 (49920 ÷ 8 = 6240) → pair (8, 6240)
8. 10 divides 49920 (49920 ÷ 10 = 4992) → pair (10, 4992)
9. 12 divides 49920 (49920 ÷ 12 = 4160) → pair (12, 4160)
10. 13 divides 49920 (49920 ÷ 13 = 3840) → pair (13, 3840)
11. 15 divides 49920 (49920 ÷ 15 = 3328) → pair (15, 3328)
12. 16 divides 49920 (49920 ÷ 16 = 3120) → pair (16, 3120)
13. 20 divides 49920 (49920 ÷ 20 = 2496) → pair (20, 2496)
14. 24 divides 49920 (49920 ÷ 24 = 2080) → pair (24, 2080)
15. 26 divides 49920 (49920 ÷ 26 = 1920) → pair (26, 1920)
16. 30 divides 49920 (49920 ÷ 30 = 1664) → pair (30, 1664)
17. 32 divides 49920 (49920 ÷ 32 = 1560) → pair (32, 1560)
18. 39 divides 49920 (49920 ÷ 39 = 1280) → pair (39, 1280)
19. 40 divides 49920 (49920 ÷ 40 = 1248) → pair (40, 1248)
20. 48 divides 49920 (49920 ÷ 48 = 1040) → pair (48, 1040)
21. 52 divides 49920 (49920 ÷ 52 = 960) → pair (52, 960)
22. 60 divides 49920 (49920 ÷ 60 = 832) → pair (60, 832)
23. 64 divides 49920 (49920 ÷ 64 = 780) → pair (64, 780)
24. 65 divides 49920 (49920 ÷ 65 = 768) → pair (65, 768)
25. 78 divides 49920 (49920 ÷ 78 = 640) → pair (78, 640)
26. 80 divides 49920 (49920 ÷ 80 = 624) → pair (80, 624)
27. 96 divides 49920 (49920 ÷ 96 = 520) → pair (96, 520)
28. 104 divides 49920 (49920 ÷ 104 = 480) → pair (104, 480)
29. 120 divides 49920 (49920 ÷ 120 = 416) → pair (120, 416)
30. 128 divides 49920 (49920 ÷ 128 = 390) → pair (128, 390)
31. 130 divides 49920 (49920 ÷ 130 = 384) → pair (130, 384)
32. 156 divides 49920 (49920 ÷ 156 = 320) → pair (156, 320)
33. 160 divides 49920 (49920 ÷ 160 = 312) → pair (160, 312)
34. 192 divides 49920 (49920 ÷ 192 = 260) → pair (192, 260)
35. 195 divides 49920 (49920 ÷ 195 = 256) → pair (195, 256)
36. 208 divides 49920 (49920 ÷ 208 = 240) → pair (208, 240)
37. Collect all unique values: {1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 16, 20, 24, 26, 30, 32, 39, 40, 48, 52, 60, 64, 65, 78, 80, 96, 104, 120, 128, 130, 156, 160, 192, 195, 208, 240, 256, 260, 312, 320, 384, 390, 416, 480, 520, 624, 640, 768, 780, 832, 960, 1040, 1248, 1280, 1560, 1664, 1920, 2080, 2496, 3120, 3328, 3840, 4160, 4992, 6240, 8320, 9984, 12480, 16640, 24960, 49920} — total 72 divisors.
38. Sum: 1 + 2 + 3 + 4 + 5 + 6 + 8 + 10 + 12 + 13 + 15 + 16 + 20 + 24 + 26 + 30 + 32 + 39 + 40 + 48 + 52 + 60 + 64 + 65 + 78 + 80 + 96 + 104 + 120 + 128 + 130 + 156 + 160 + 192 + 195 + 208 + 240 + 256 + 260 + 312 + 320 + 384 + 390 + 416 + 480 + 520 + 624 + 640 + 768 + 780 + 832 + 960 + 1040 + 1248 + 1280 + 1560 + 1664 + 1920 + 2080 + 2496 + 3120 + 3328 + 3840 + 4160 + 4992 + 6240 + 8320 + 9984 + 12480 + 16640 + 24960 + 49920 = 171696.

Nearby Examples

Related Operations for 49920

• Multiples of a Number — "outward" complement of divisors
• 49920 Prime Factorization — decompose into prime building blocks
• Find GCF of 49920 and another number
• Find LCM of 49920 and another number
• Is 49920 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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