Divisors of 9600: All 48 Factors

Quick Answer

9600 has 48 divisors (factors): 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, 128, 150, 160, 192, 200, 240, 300, 320, 384, 400, 480, 600, 640, 800, 960, 1200, 1600, 1920, 2400, 3200, 4800, 9600.

Sum: 31620.

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, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 64, 75, 80, 96, 100, 120, 128, 150, 160, 192, 200, 240, 300, 320, 384, 400, 480, 600, 640, 800, 960, 1200, 1600, 1920, 2400, 3200, 4800, 9600

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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 9600

The number 9600 has 48 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,  128,  150,  160,  192,  200,  240,  300,  320,  384,  400,  480,  600,  640,  800,  960,  1200,  1600,  1920,  2400,  3200,  4800,  9600

Divisor Pairs of 9600

Each pair multiplies to 9600:

Factor 1×Factor 2=Product
1×9600=9600
2×4800=9600
3×3200=9600
4×2400=9600
5×1920=9600
6×1600=9600
8×1200=9600
10×960=9600
12×800=9600
15×640=9600
16×600=9600
20×480=9600
24×400=9600
25×384=9600
30×320=9600
32×300=9600
40×240=9600
48×200=9600
50×192=9600
60×160=9600
64×150=9600
75×128=9600
80×120=9600
96×100=9600

Number of Divisors

The number 9600 has 48 divisors, written as τ(9600) = 48 in number theory.

Sum of Divisors

σ(9600) = 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 + 128 + 150 + 160 + 192 + 200 + 240 + 300 + 320 + 384 + 400 + 480 + 600 + 640 + 800 + 960 + 1200 + 1600 + 1920 + 2400 + 3200 + 4800 + 9600 = 31620

Prime Factorization of 9600

See the full prime factorization calculator →

Properties of 9600

  • 9600 is composite.
  • 9600 is not a perfect square.
  • Number of divisors: 48.
  • Sum of divisors: 31620.

Common Divisors with Another Number?

Looking for the divisors that 9600 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 9600

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √9600 ≈ 97.98. If i divides 9600, then both i and 9600/i are divisors.

  1. 1 divides 9600 (9600 ÷ 1 = 9600) → pair (1, 9600)
  2. 2 divides 9600 (9600 ÷ 2 = 4800) → pair (2, 4800)
  3. 3 divides 9600 (9600 ÷ 3 = 3200) → pair (3, 3200)
  4. 4 divides 9600 (9600 ÷ 4 = 2400) → pair (4, 2400)
  5. 5 divides 9600 (9600 ÷ 5 = 1920) → pair (5, 1920)
  6. 6 divides 9600 (9600 ÷ 6 = 1600) → pair (6, 1600)
  7. 8 divides 9600 (9600 ÷ 8 = 1200) → pair (8, 1200)
  8. 10 divides 9600 (9600 ÷ 10 = 960) → pair (10, 960)
  9. 12 divides 9600 (9600 ÷ 12 = 800) → pair (12, 800)
  10. 15 divides 9600 (9600 ÷ 15 = 640) → pair (15, 640)
  11. 16 divides 9600 (9600 ÷ 16 = 600) → pair (16, 600)
  12. 20 divides 9600 (9600 ÷ 20 = 480) → pair (20, 480)
  13. 24 divides 9600 (9600 ÷ 24 = 400) → pair (24, 400)
  14. 25 divides 9600 (9600 ÷ 25 = 384) → pair (25, 384)
  15. 30 divides 9600 (9600 ÷ 30 = 320) → pair (30, 320)
  16. 32 divides 9600 (9600 ÷ 32 = 300) → pair (32, 300)
  17. 40 divides 9600 (9600 ÷ 40 = 240) → pair (40, 240)
  18. 48 divides 9600 (9600 ÷ 48 = 200) → pair (48, 200)
  19. 50 divides 9600 (9600 ÷ 50 = 192) → pair (50, 192)
  20. 60 divides 9600 (9600 ÷ 60 = 160) → pair (60, 160)
  21. 64 divides 9600 (9600 ÷ 64 = 150) → pair (64, 150)
  22. 75 divides 9600 (9600 ÷ 75 = 128) → pair (75, 128)
  23. 80 divides 9600 (9600 ÷ 80 = 120) → pair (80, 120)
  24. 96 divides 9600 (9600 ÷ 96 = 100) → pair (96, 100)
  25. 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, 128, 150, 160, 192, 200, 240, 300, 320, 384, 400, 480, 600, 640, 800, 960, 1200, 1600, 1920, 2400, 3200, 4800, 9600} — total 48 divisors.
  26. 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 + 128 + 150 + 160 + 192 + 200 + 240 + 300 + 320 + 384 + 400 + 480 + 600 + 640 + 800 + 960 + 1200 + 1600 + 1920 + 2400 + 3200 + 4800 + 9600 = 31620.

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Related Operations for 9600

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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