Divisors of 5184: All 35 Factors

Divisors (Factors) Calculator

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 5184

The number 5184 has 35 divisors:

1,  2,  3,  4,  6,  8,  9,  12,  16,  18,  24,  27,  32,  36,  48,  54,  64,  72,  81,  96,  108,  144,  162,  192,  216,  288,  324,  432,  576,  648,  864,  1296,  1728,  2592,  5184

Divisor Pairs of 5184

Each pair multiplies to 5184:

Note: the last pair has identical factors (72 × 72) because 5184 is a perfect square.

Number of Divisors

The number 5184 has 35 divisors, written as τ(5184) = 35 in number theory.

⚡ Notice: 5184 has an odd number of divisors — this means 5184 is a perfect square (√5184 = 72).

Sum of Divisors

σ(5184) = 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 16 + 18 + 24 + 27 + 32 + 36 + 48 + 54 + 64 + 72 + 81 + 96 + 108 + 144 + 162 + 192 + 216 + 288 + 324 + 432 + 576 + 648 + 864 + 1296 + 1728 + 2592 + 5184 = 15367

Prime Factorization of 5184

See the full prime factorization calculator →

Properties of 5184

• 5184 is composite.
• 5184 is a perfect square (√5184 = 72).
• Number of divisors: 35.
• Sum of divisors: 15367.

Common Divisors with Another Number?

Looking for the divisors that 5184 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 5184

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √5184 ≈ 72.00. If i divides 5184, then both i and 5184/i are divisors.

1. 1 divides 5184 (5184 ÷ 1 = 5184) → pair (1, 5184)
2. 2 divides 5184 (5184 ÷ 2 = 2592) → pair (2, 2592)
3. 3 divides 5184 (5184 ÷ 3 = 1728) → pair (3, 1728)
4. 4 divides 5184 (5184 ÷ 4 = 1296) → pair (4, 1296)
5. 6 divides 5184 (5184 ÷ 6 = 864) → pair (6, 864)
6. 8 divides 5184 (5184 ÷ 8 = 648) → pair (8, 648)
7. 9 divides 5184 (5184 ÷ 9 = 576) → pair (9, 576)
8. 12 divides 5184 (5184 ÷ 12 = 432) → pair (12, 432)
9. 16 divides 5184 (5184 ÷ 16 = 324) → pair (16, 324)
10. 18 divides 5184 (5184 ÷ 18 = 288) → pair (18, 288)
11. 24 divides 5184 (5184 ÷ 24 = 216) → pair (24, 216)
12. 27 divides 5184 (5184 ÷ 27 = 192) → pair (27, 192)
13. 32 divides 5184 (5184 ÷ 32 = 162) → pair (32, 162)
14. 36 divides 5184 (5184 ÷ 36 = 144) → pair (36, 144)
15. 48 divides 5184 (5184 ÷ 48 = 108) → pair (48, 108)
16. 54 divides 5184 (5184 ÷ 54 = 96) → pair (54, 96)
17. 64 divides 5184 (5184 ÷ 64 = 81) → pair (64, 81)
18. 72 divides 5184 (5184 ÷ 72 = 72) → pair (72, 72)
19. Collect all unique values: {1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 81, 96, 108, 144, 162, 192, 216, 288, 324, 432, 576, 648, 864, 1296, 1728, 2592, 5184} — total 35 divisors.
20. Sum: 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 16 + 18 + 24 + 27 + 32 + 36 + 48 + 54 + 64 + 72 + 81 + 96 + 108 + 144 + 162 + 192 + 216 + 288 + 324 + 432 + 576 + 648 + 864 + 1296 + 1728 + 2592 + 5184 = 15367.

Nearby Examples

Related Operations for 5184

• Multiples of 5184 — "outward" complement; M is a multiple of 5184 ⇔ 5184 is a divisor of M
• 5184 Prime Factorization — decompose into prime building blocks
• Find GCF of 5184 and another number
• Find LCM of 5184 and another number
• Is 5184 a perfect square? (odd divisor count ⇔ yes)

See also our tables of divisors:

• Table of all divisors from 1 to 100
• Table of all divisors from 1 to 500
• Table of all divisors from 1 to 1,000
• Table of all divisors from 1 to 10,000

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

• [1] Divisor (Wikipedia)
• [2] Divisor function (Wikipedia)
• [3] Divisor (Wolfram MathWorld)

Divisors Calculation Examples

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