Divisors of 9000: All 48 Factors

Quick Answer

9000 has 48 divisors (factors): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 30, 36, 40, 45, 50, 60, 72, 75, 90, 100, 120, 125, 150, 180, 200, 225, 250, 300, 360, 375, 450, 500, 600, 750, 900, 1000, 1125, 1500, 1800, 2250, 3000, 4500, 9000.

Sum: 30420.

Divisors (Factors) Calculator

Divisors Multiples Prime Factoriz. GCF LCM

  Ex.: 12, 36, 100, 1024, 1728, etc.
48 divisors
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 30, 36, 40, 45, 50, 60, 72, 75, 90, 100, 120, 125, 150, 180, 200, 225, 250, 300, 360, 375, 450, 500, 600, 750, 900, 1000, 1125, 1500, 1800, 2250, 3000, 4500, 9000

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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 9000

The number 9000 has 48 divisors:

1,  2,  3,  4,  5,  6,  8,  9,  10,  12,  15,  18,  20,  24,  25,  30,  36,  40,  45,  50,  60,  72,  75,  90,  100,  120,  125,  150,  180,  200,  225,  250,  300,  360,  375,  450,  500,  600,  750,  900,  1000,  1125,  1500,  1800,  2250,  3000,  4500,  9000

Divisor Pairs of 9000

Each pair multiplies to 9000:

Factor 1×Factor 2=Product
1×9000=9000
2×4500=9000
3×3000=9000
4×2250=9000
5×1800=9000
6×1500=9000
8×1125=9000
9×1000=9000
10×900=9000
12×750=9000
15×600=9000
18×500=9000
20×450=9000
24×375=9000
25×360=9000
30×300=9000
36×250=9000
40×225=9000
45×200=9000
50×180=9000
60×150=9000
72×125=9000
75×120=9000
90×100=9000

Number of Divisors

The number 9000 has 48 divisors, written as τ(9000) = 48 in number theory.

Sum of Divisors

σ(9000) = 1 + 2 + 3 + 4 + 5 + 6 + 8 + 9 + 10 + 12 + 15 + 18 + 20 + 24 + 25 + 30 + 36 + 40 + 45 + 50 + 60 + 72 + 75 + 90 + 100 + 120 + 125 + 150 + 180 + 200 + 225 + 250 + 300 + 360 + 375 + 450 + 500 + 600 + 750 + 900 + 1000 + 1125 + 1500 + 1800 + 2250 + 3000 + 4500 + 9000 = 30420

Prime Factorization of 9000

See the full prime factorization calculator →

Properties of 9000

  • 9000 is composite.
  • 9000 is not a perfect square.
  • Number of divisors: 48.
  • Sum of divisors: 30420.

Common Divisors with Another Number?

Looking for the divisors that 9000 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 9000

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √9000 ≈ 94.87. If i divides 9000, then both i and 9000/i are divisors.

  1. 1 divides 9000 (9000 ÷ 1 = 9000) → pair (1, 9000)
  2. 2 divides 9000 (9000 ÷ 2 = 4500) → pair (2, 4500)
  3. 3 divides 9000 (9000 ÷ 3 = 3000) → pair (3, 3000)
  4. 4 divides 9000 (9000 ÷ 4 = 2250) → pair (4, 2250)
  5. 5 divides 9000 (9000 ÷ 5 = 1800) → pair (5, 1800)
  6. 6 divides 9000 (9000 ÷ 6 = 1500) → pair (6, 1500)
  7. 8 divides 9000 (9000 ÷ 8 = 1125) → pair (8, 1125)
  8. 9 divides 9000 (9000 ÷ 9 = 1000) → pair (9, 1000)
  9. 10 divides 9000 (9000 ÷ 10 = 900) → pair (10, 900)
  10. 12 divides 9000 (9000 ÷ 12 = 750) → pair (12, 750)
  11. 15 divides 9000 (9000 ÷ 15 = 600) → pair (15, 600)
  12. 18 divides 9000 (9000 ÷ 18 = 500) → pair (18, 500)
  13. 20 divides 9000 (9000 ÷ 20 = 450) → pair (20, 450)
  14. 24 divides 9000 (9000 ÷ 24 = 375) → pair (24, 375)
  15. 25 divides 9000 (9000 ÷ 25 = 360) → pair (25, 360)
  16. 30 divides 9000 (9000 ÷ 30 = 300) → pair (30, 300)
  17. 36 divides 9000 (9000 ÷ 36 = 250) → pair (36, 250)
  18. 40 divides 9000 (9000 ÷ 40 = 225) → pair (40, 225)
  19. 45 divides 9000 (9000 ÷ 45 = 200) → pair (45, 200)
  20. 50 divides 9000 (9000 ÷ 50 = 180) → pair (50, 180)
  21. 60 divides 9000 (9000 ÷ 60 = 150) → pair (60, 150)
  22. 72 divides 9000 (9000 ÷ 72 = 125) → pair (72, 125)
  23. 75 divides 9000 (9000 ÷ 75 = 120) → pair (75, 120)
  24. 90 divides 9000 (9000 ÷ 90 = 100) → pair (90, 100)
  25. Collect all unique values: {1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 30, 36, 40, 45, 50, 60, 72, 75, 90, 100, 120, 125, 150, 180, 200, 225, 250, 300, 360, 375, 450, 500, 600, 750, 900, 1000, 1125, 1500, 1800, 2250, 3000, 4500, 9000} — total 48 divisors.
  26. Sum: 1 + 2 + 3 + 4 + 5 + 6 + 8 + 9 + 10 + 12 + 15 + 18 + 20 + 24 + 25 + 30 + 36 + 40 + 45 + 50 + 60 + 72 + 75 + 90 + 100 + 120 + 125 + 150 + 180 + 200 + 225 + 250 + 300 + 360 + 375 + 450 + 500 + 600 + 750 + 900 + 1000 + 1125 + 1500 + 1800 + 2250 + 3000 + 4500 + 9000 = 30420.

Nearby Examples

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Related Operations for 9000

See also our tables of divisors:

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

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