Divisors of 13500: All 48 Factors

Quick Answer

13500 has 48 divisors (factors): 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 27, 30, 36, 45, 50, 54, 60, 75, 90, 100, 108, 125, 135, 150, 180, 225, 250, 270, 300, 375, 450, 500, 540, 675, 750, 900, 1125, 1350, 1500, 2250, 2700, 3375, 4500, 6750, 13500.

Sum: 43680.

Divisors (Factors) Calculator

Divisors Multiples Prime Factoriz. GCF LCM

  Ex.: 12, 36, 100, 1024, 1728, etc.
48 divisors
1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 27, 30, 36, 45, 50, 54, 60, 75, 90, 100, 108, 125, 135, 150, 180, 225, 250, 270, 300, 375, 450, 500, 540, 675, 750, 900, 1125, 1350, 1500, 2250, 2700, 3375, 4500, 6750, 13500

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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 13500

The number 13500 has 48 divisors:

1,  2,  3,  4,  5,  6,  9,  10,  12,  15,  18,  20,  25,  27,  30,  36,  45,  50,  54,  60,  75,  90,  100,  108,  125,  135,  150,  180,  225,  250,  270,  300,  375,  450,  500,  540,  675,  750,  900,  1125,  1350,  1500,  2250,  2700,  3375,  4500,  6750,  13500

Divisor Pairs of 13500

Each pair multiplies to 13500:

Factor 1×Factor 2=Product
1×13500=13500
2×6750=13500
3×4500=13500
4×3375=13500
5×2700=13500
6×2250=13500
9×1500=13500
10×1350=13500
12×1125=13500
15×900=13500
18×750=13500
20×675=13500
25×540=13500
27×500=13500
30×450=13500
36×375=13500
45×300=13500
50×270=13500
54×250=13500
60×225=13500
75×180=13500
90×150=13500
100×135=13500
108×125=13500

Number of Divisors

The number 13500 has 48 divisors, written as τ(13500) = 48 in number theory.

Sum of Divisors

σ(13500) = 1 + 2 + 3 + 4 + 5 + 6 + 9 + 10 + 12 + 15 + 18 + 20 + 25 + 27 + 30 + 36 + 45 + 50 + 54 + 60 + 75 + 90 + 100 + 108 + 125 + 135 + 150 + 180 + 225 + 250 + 270 + 300 + 375 + 450 + 500 + 540 + 675 + 750 + 900 + 1125 + 1350 + 1500 + 2250 + 2700 + 3375 + 4500 + 6750 + 13500 = 43680

Prime Factorization of 13500

See the full prime factorization calculator →

Properties of 13500

  • 13500 is composite.
  • 13500 is not a perfect square.
  • Number of divisors: 48.
  • Sum of divisors: 43680.

Common Divisors with Another Number?

Looking for the divisors that 13500 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 13500

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √13500 ≈ 116.19. If i divides 13500, then both i and 13500/i are divisors.

  1. 1 divides 13500 (13500 ÷ 1 = 13500) → pair (1, 13500)
  2. 2 divides 13500 (13500 ÷ 2 = 6750) → pair (2, 6750)
  3. 3 divides 13500 (13500 ÷ 3 = 4500) → pair (3, 4500)
  4. 4 divides 13500 (13500 ÷ 4 = 3375) → pair (4, 3375)
  5. 5 divides 13500 (13500 ÷ 5 = 2700) → pair (5, 2700)
  6. 6 divides 13500 (13500 ÷ 6 = 2250) → pair (6, 2250)
  7. 9 divides 13500 (13500 ÷ 9 = 1500) → pair (9, 1500)
  8. 10 divides 13500 (13500 ÷ 10 = 1350) → pair (10, 1350)
  9. 12 divides 13500 (13500 ÷ 12 = 1125) → pair (12, 1125)
  10. 15 divides 13500 (13500 ÷ 15 = 900) → pair (15, 900)
  11. 18 divides 13500 (13500 ÷ 18 = 750) → pair (18, 750)
  12. 20 divides 13500 (13500 ÷ 20 = 675) → pair (20, 675)
  13. 25 divides 13500 (13500 ÷ 25 = 540) → pair (25, 540)
  14. 27 divides 13500 (13500 ÷ 27 = 500) → pair (27, 500)
  15. 30 divides 13500 (13500 ÷ 30 = 450) → pair (30, 450)
  16. 36 divides 13500 (13500 ÷ 36 = 375) → pair (36, 375)
  17. 45 divides 13500 (13500 ÷ 45 = 300) → pair (45, 300)
  18. 50 divides 13500 (13500 ÷ 50 = 270) → pair (50, 270)
  19. 54 divides 13500 (13500 ÷ 54 = 250) → pair (54, 250)
  20. 60 divides 13500 (13500 ÷ 60 = 225) → pair (60, 225)
  21. 75 divides 13500 (13500 ÷ 75 = 180) → pair (75, 180)
  22. 90 divides 13500 (13500 ÷ 90 = 150) → pair (90, 150)
  23. 100 divides 13500 (13500 ÷ 100 = 135) → pair (100, 135)
  24. 108 divides 13500 (13500 ÷ 108 = 125) → pair (108, 125)
  25. Collect all unique values: {1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 27, 30, 36, 45, 50, 54, 60, 75, 90, 100, 108, 125, 135, 150, 180, 225, 250, 270, 300, 375, 450, 500, 540, 675, 750, 900, 1125, 1350, 1500, 2250, 2700, 3375, 4500, 6750, 13500} — total 48 divisors.
  26. Sum: 1 + 2 + 3 + 4 + 5 + 6 + 9 + 10 + 12 + 15 + 18 + 20 + 25 + 27 + 30 + 36 + 45 + 50 + 54 + 60 + 75 + 90 + 100 + 108 + 125 + 135 + 150 + 180 + 225 + 250 + 270 + 300 + 375 + 450 + 500 + 540 + 675 + 750 + 900 + 1125 + 1350 + 1500 + 2250 + 2700 + 3375 + 4500 + 6750 + 13500 = 43680.

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Related Operations for 13500

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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