Divisors of 9900: All 54 Factors

Quick Answer

9900 has 54 divisors (factors): 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 25, 30, 33, 36, 44, 45, 50, 55, 60, 66, 75, 90, 99, 100, 110, 132, 150, 165, 180, 198, 220, 225, 275, 300, 330, 396, 450, 495, 550, 660, 825, 900, 990, 1100, 1650, 1980, 2475, 3300, 4950, 9900.

Sum: 33852.

Divisors (Factors) Calculator

Divisors Multiples Prime Factoriz. GCF LCM

  Ex.: 12, 36, 100, 1024, 1728, etc.
54 divisors
1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 25, 30, 33, 36, 44, 45, 50, 55, 60, 66, 75, 90, 99, 100, 110, 132, 150, 165, 180, 198, 220, 225, 275, 300, 330, 396, 450, 495, 550, 660, 825, 900, 990, 1100, 1650, 1980, 2475, 3300, 4950, 9900

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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 9900

The number 9900 has 54 divisors:

1,  2,  3,  4,  5,  6,  9,  10,  11,  12,  15,  18,  20,  22,  25,  30,  33,  36,  44,  45,  50,  55,  60,  66,  75,  90,  99,  100,  110,  132,  150,  165,  180,  198,  220,  225,  275,  300,  330,  396,  450,  495,  550,  660,  825,  900,  990,  1100,  1650,  1980,  2475,  3300,  4950,  9900

Divisor Pairs of 9900

Each pair multiplies to 9900:

Factor 1×Factor 2=Product
1×9900=9900
2×4950=9900
3×3300=9900
4×2475=9900
5×1980=9900
6×1650=9900
9×1100=9900
10×990=9900
11×900=9900
12×825=9900
15×660=9900
18×550=9900
20×495=9900
22×450=9900
25×396=9900
30×330=9900
33×300=9900
36×275=9900
44×225=9900
45×220=9900
50×198=9900
55×180=9900
60×165=9900
66×150=9900
75×132=9900
90×110=9900
99×100=9900

Number of Divisors

The number 9900 has 54 divisors, written as τ(9900) = 54 in number theory.

Sum of Divisors

σ(9900) = 1 + 2 + 3 + 4 + 5 + 6 + 9 + 10 + 11 + 12 + 15 + 18 + 20 + 22 + 25 + 30 + 33 + 36 + 44 + 45 + 50 + 55 + 60 + 66 + 75 + 90 + 99 + 100 + 110 + 132 + 150 + 165 + 180 + 198 + 220 + 225 + 275 + 300 + 330 + 396 + 450 + 495 + 550 + 660 + 825 + 900 + 990 + 1100 + 1650 + 1980 + 2475 + 3300 + 4950 + 9900 = 33852

Prime Factorization of 9900

See the full prime factorization calculator →

Properties of 9900

  • 9900 is composite.
  • 9900 is not a perfect square.
  • Number of divisors: 54.
  • Sum of divisors: 33852.

Common Divisors with Another Number?

Looking for the divisors that 9900 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 9900

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √9900 ≈ 99.50. If i divides 9900, then both i and 9900/i are divisors.

  1. 1 divides 9900 (9900 ÷ 1 = 9900) → pair (1, 9900)
  2. 2 divides 9900 (9900 ÷ 2 = 4950) → pair (2, 4950)
  3. 3 divides 9900 (9900 ÷ 3 = 3300) → pair (3, 3300)
  4. 4 divides 9900 (9900 ÷ 4 = 2475) → pair (4, 2475)
  5. 5 divides 9900 (9900 ÷ 5 = 1980) → pair (5, 1980)
  6. 6 divides 9900 (9900 ÷ 6 = 1650) → pair (6, 1650)
  7. 9 divides 9900 (9900 ÷ 9 = 1100) → pair (9, 1100)
  8. 10 divides 9900 (9900 ÷ 10 = 990) → pair (10, 990)
  9. 11 divides 9900 (9900 ÷ 11 = 900) → pair (11, 900)
  10. 12 divides 9900 (9900 ÷ 12 = 825) → pair (12, 825)
  11. 15 divides 9900 (9900 ÷ 15 = 660) → pair (15, 660)
  12. 18 divides 9900 (9900 ÷ 18 = 550) → pair (18, 550)
  13. 20 divides 9900 (9900 ÷ 20 = 495) → pair (20, 495)
  14. 22 divides 9900 (9900 ÷ 22 = 450) → pair (22, 450)
  15. 25 divides 9900 (9900 ÷ 25 = 396) → pair (25, 396)
  16. 30 divides 9900 (9900 ÷ 30 = 330) → pair (30, 330)
  17. 33 divides 9900 (9900 ÷ 33 = 300) → pair (33, 300)
  18. 36 divides 9900 (9900 ÷ 36 = 275) → pair (36, 275)
  19. 44 divides 9900 (9900 ÷ 44 = 225) → pair (44, 225)
  20. 45 divides 9900 (9900 ÷ 45 = 220) → pair (45, 220)
  21. 50 divides 9900 (9900 ÷ 50 = 198) → pair (50, 198)
  22. 55 divides 9900 (9900 ÷ 55 = 180) → pair (55, 180)
  23. 60 divides 9900 (9900 ÷ 60 = 165) → pair (60, 165)
  24. 66 divides 9900 (9900 ÷ 66 = 150) → pair (66, 150)
  25. 75 divides 9900 (9900 ÷ 75 = 132) → pair (75, 132)
  26. 90 divides 9900 (9900 ÷ 90 = 110) → pair (90, 110)
  27. 99 divides 9900 (9900 ÷ 99 = 100) → pair (99, 100)
  28. Collect all unique values: {1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 25, 30, 33, 36, 44, 45, 50, 55, 60, 66, 75, 90, 99, 100, 110, 132, 150, 165, 180, 198, 220, 225, 275, 300, 330, 396, 450, 495, 550, 660, 825, 900, 990, 1100, 1650, 1980, 2475, 3300, 4950, 9900} — total 54 divisors.
  29. Sum: 1 + 2 + 3 + 4 + 5 + 6 + 9 + 10 + 11 + 12 + 15 + 18 + 20 + 22 + 25 + 30 + 33 + 36 + 44 + 45 + 50 + 55 + 60 + 66 + 75 + 90 + 99 + 100 + 110 + 132 + 150 + 165 + 180 + 198 + 220 + 225 + 275 + 300 + 330 + 396 + 450 + 495 + 550 + 660 + 825 + 900 + 990 + 1100 + 1650 + 1980 + 2475 + 3300 + 4950 + 9900 = 33852.

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Related Operations for 9900

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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