Divisors of 48000: All 64 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 48000

The number 48000 has 64 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,  125,  128,  150,  160,  192,  200,  240,  250,  300,  320,  375,  384,  400,  480,  500,  600,  640,  750,  800,  960,  1000,  1200,  1500,  1600,  1920,  2000,  2400,  3000,  3200,  4000,  4800,  6000,  8000,  9600,  12000,  16000,  24000,  48000

Divisor Pairs of 48000

Each pair multiplies to 48000:

Number of Divisors

The number 48000 has 64 divisors, written as τ(48000) = 64 in number theory.

Sum of Divisors

σ(48000) = 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 + 125 + 128 + 150 + 160 + 192 + 200 + 240 + 250 + 300 + 320 + 375 + 384 + 400 + 480 + 500 + 600 + 640 + 750 + 800 + 960 + 1000 + 1200 + 1500 + 1600 + 1920 + 2000 + 2400 + 3000 + 3200 + 4000 + 4800 + 6000 + 8000 + 9600 + 12000 + 16000 + 24000 + 48000 = 159120

Prime Factorization of 48000

See the full prime factorization calculator →

Properties of 48000

• 48000 is composite.
• 48000 is not a perfect square.
• Number of divisors: 64.
• Sum of divisors: 159120.

Common Divisors with Another Number?

Looking for the divisors that 48000 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 48000

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √48000 ≈ 219.09. If i divides 48000, then both i and 48000/i are divisors.

1. 1 divides 48000 (48000 ÷ 1 = 48000) → pair (1, 48000)
2. 2 divides 48000 (48000 ÷ 2 = 24000) → pair (2, 24000)
3. 3 divides 48000 (48000 ÷ 3 = 16000) → pair (3, 16000)
4. 4 divides 48000 (48000 ÷ 4 = 12000) → pair (4, 12000)
5. 5 divides 48000 (48000 ÷ 5 = 9600) → pair (5, 9600)
6. 6 divides 48000 (48000 ÷ 6 = 8000) → pair (6, 8000)
7. 8 divides 48000 (48000 ÷ 8 = 6000) → pair (8, 6000)
8. 10 divides 48000 (48000 ÷ 10 = 4800) → pair (10, 4800)
9. 12 divides 48000 (48000 ÷ 12 = 4000) → pair (12, 4000)
10. 15 divides 48000 (48000 ÷ 15 = 3200) → pair (15, 3200)
11. 16 divides 48000 (48000 ÷ 16 = 3000) → pair (16, 3000)
12. 20 divides 48000 (48000 ÷ 20 = 2400) → pair (20, 2400)
13. 24 divides 48000 (48000 ÷ 24 = 2000) → pair (24, 2000)
14. 25 divides 48000 (48000 ÷ 25 = 1920) → pair (25, 1920)
15. 30 divides 48000 (48000 ÷ 30 = 1600) → pair (30, 1600)
16. 32 divides 48000 (48000 ÷ 32 = 1500) → pair (32, 1500)
17. 40 divides 48000 (48000 ÷ 40 = 1200) → pair (40, 1200)
18. 48 divides 48000 (48000 ÷ 48 = 1000) → pair (48, 1000)
19. 50 divides 48000 (48000 ÷ 50 = 960) → pair (50, 960)
20. 60 divides 48000 (48000 ÷ 60 = 800) → pair (60, 800)
21. 64 divides 48000 (48000 ÷ 64 = 750) → pair (64, 750)
22. 75 divides 48000 (48000 ÷ 75 = 640) → pair (75, 640)
23. 80 divides 48000 (48000 ÷ 80 = 600) → pair (80, 600)
24. 96 divides 48000 (48000 ÷ 96 = 500) → pair (96, 500)
25. 100 divides 48000 (48000 ÷ 100 = 480) → pair (100, 480)
26. 120 divides 48000 (48000 ÷ 120 = 400) → pair (120, 400)
27. 125 divides 48000 (48000 ÷ 125 = 384) → pair (125, 384)
28. 128 divides 48000 (48000 ÷ 128 = 375) → pair (128, 375)
29. 150 divides 48000 (48000 ÷ 150 = 320) → pair (150, 320)
30. 160 divides 48000 (48000 ÷ 160 = 300) → pair (160, 300)
31. 192 divides 48000 (48000 ÷ 192 = 250) → pair (192, 250)
32. 200 divides 48000 (48000 ÷ 200 = 240) → pair (200, 240)
33. 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, 125, 128, 150, 160, 192, 200, 240, 250, 300, 320, 375, 384, 400, 480, 500, 600, 640, 750, 800, 960, 1000, 1200, 1500, 1600, 1920, 2000, 2400, 3000, 3200, 4000, 4800, 6000, 8000, 9600, 12000, 16000, 24000, 48000} — total 64 divisors.
34. 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 + 125 + 128 + 150 + 160 + 192 + 200 + 240 + 250 + 300 + 320 + 375 + 384 + 400 + 480 + 500 + 600 + 640 + 750 + 800 + 960 + 1000 + 1200 + 1500 + 1600 + 1920 + 2000 + 2400 + 3000 + 3200 + 4000 + 4800 + 6000 + 8000 + 9600 + 12000 + 16000 + 24000 + 48000 = 159120.

Nearby Examples

Related Operations for 48000

• Multiples of a Number — "outward" complement of divisors
• 48000 Prime Factorization — decompose into prime building blocks
• Find GCF of 48000 and another number
• Find LCM of 48000 and another number
• Is 48000 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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