Divisors of 5460: All 48 Factors

Quick Answer

5460 has 48 divisors (factors): 1, 2, 3, 4, 5, 6, 7, 10, 12, 13, 14, 15, 20, 21, 26, 28, 30, 35, 39, 42, 52, 60, 65, 70, 78, 84, 91, 105, 130, 140, 156, 182, 195, 210, 260, 273, 364, 390, 420, 455, 546, 780, 910, 1092, 1365, 1820, 2730, 5460.

Sum: 18816.

Divisors (Factors) Calculator

Divisors Multiples Prime Factoriz. GCF LCM

  Ex.: 12, 36, 100, 1024, 1728, etc.
48 divisors
1, 2, 3, 4, 5, 6, 7, 10, 12, 13, 14, 15, 20, 21, 26, 28, 30, 35, 39, 42, 52, 60, 65, 70, 78, 84, 91, 105, 130, 140, 156, 182, 195, 210, 260, 273, 364, 390, 420, 455, 546, 780, 910, 1092, 1365, 1820, 2730, 5460

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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 5460

The number 5460 has 48 divisors:

1,  2,  3,  4,  5,  6,  7,  10,  12,  13,  14,  15,  20,  21,  26,  28,  30,  35,  39,  42,  52,  60,  65,  70,  78,  84,  91,  105,  130,  140,  156,  182,  195,  210,  260,  273,  364,  390,  420,  455,  546,  780,  910,  1092,  1365,  1820,  2730,  5460

Divisor Pairs of 5460

Each pair multiplies to 5460:

Factor 1×Factor 2=Product
1×5460=5460
2×2730=5460
3×1820=5460
4×1365=5460
5×1092=5460
6×910=5460
7×780=5460
10×546=5460
12×455=5460
13×420=5460
14×390=5460
15×364=5460
20×273=5460
21×260=5460
26×210=5460
28×195=5460
30×182=5460
35×156=5460
39×140=5460
42×130=5460
52×105=5460
60×91=5460
65×84=5460
70×78=5460

Number of Divisors

The number 5460 has 48 divisors, written as τ(5460) = 48 in number theory.

Sum of Divisors

σ(5460) = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 10 + 12 + 13 + 14 + 15 + 20 + 21 + 26 + 28 + 30 + 35 + 39 + 42 + 52 + 60 + 65 + 70 + 78 + 84 + 91 + 105 + 130 + 140 + 156 + 182 + 195 + 210 + 260 + 273 + 364 + 390 + 420 + 455 + 546 + 780 + 910 + 1092 + 1365 + 1820 + 2730 + 5460 = 18816

Prime Factorization of 5460

See the full prime factorization calculator →

Properties of 5460

  • 5460 is composite.
  • 5460 is not a perfect square.
  • Number of divisors: 48.
  • Sum of divisors: 18816.

Common Divisors with Another Number?

Looking for the divisors that 5460 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 5460

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √5460 ≈ 73.89. If i divides 5460, then both i and 5460/i are divisors.

  1. 1 divides 5460 (5460 ÷ 1 = 5460) → pair (1, 5460)
  2. 2 divides 5460 (5460 ÷ 2 = 2730) → pair (2, 2730)
  3. 3 divides 5460 (5460 ÷ 3 = 1820) → pair (3, 1820)
  4. 4 divides 5460 (5460 ÷ 4 = 1365) → pair (4, 1365)
  5. 5 divides 5460 (5460 ÷ 5 = 1092) → pair (5, 1092)
  6. 6 divides 5460 (5460 ÷ 6 = 910) → pair (6, 910)
  7. 7 divides 5460 (5460 ÷ 7 = 780) → pair (7, 780)
  8. 10 divides 5460 (5460 ÷ 10 = 546) → pair (10, 546)
  9. 12 divides 5460 (5460 ÷ 12 = 455) → pair (12, 455)
  10. 13 divides 5460 (5460 ÷ 13 = 420) → pair (13, 420)
  11. 14 divides 5460 (5460 ÷ 14 = 390) → pair (14, 390)
  12. 15 divides 5460 (5460 ÷ 15 = 364) → pair (15, 364)
  13. 20 divides 5460 (5460 ÷ 20 = 273) → pair (20, 273)
  14. 21 divides 5460 (5460 ÷ 21 = 260) → pair (21, 260)
  15. 26 divides 5460 (5460 ÷ 26 = 210) → pair (26, 210)
  16. 28 divides 5460 (5460 ÷ 28 = 195) → pair (28, 195)
  17. 30 divides 5460 (5460 ÷ 30 = 182) → pair (30, 182)
  18. 35 divides 5460 (5460 ÷ 35 = 156) → pair (35, 156)
  19. 39 divides 5460 (5460 ÷ 39 = 140) → pair (39, 140)
  20. 42 divides 5460 (5460 ÷ 42 = 130) → pair (42, 130)
  21. 52 divides 5460 (5460 ÷ 52 = 105) → pair (52, 105)
  22. 60 divides 5460 (5460 ÷ 60 = 91) → pair (60, 91)
  23. 65 divides 5460 (5460 ÷ 65 = 84) → pair (65, 84)
  24. 70 divides 5460 (5460 ÷ 70 = 78) → pair (70, 78)
  25. Collect all unique values: {1, 2, 3, 4, 5, 6, 7, 10, 12, 13, 14, 15, 20, 21, 26, 28, 30, 35, 39, 42, 52, 60, 65, 70, 78, 84, 91, 105, 130, 140, 156, 182, 195, 210, 260, 273, 364, 390, 420, 455, 546, 780, 910, 1092, 1365, 1820, 2730, 5460} — total 48 divisors.
  26. Sum: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 10 + 12 + 13 + 14 + 15 + 20 + 21 + 26 + 28 + 30 + 35 + 39 + 42 + 52 + 60 + 65 + 70 + 78 + 84 + 91 + 105 + 130 + 140 + 156 + 182 + 195 + 210 + 260 + 273 + 364 + 390 + 420 + 455 + 546 + 780 + 910 + 1092 + 1365 + 1820 + 2730 + 5460 = 18816.

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Related Operations for 5460

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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