Divisors of 1728: All 28 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 1728

The number 1728 has 28 divisors:

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

Divisor Pairs of 1728

Each pair multiplies to 1728:

Number of Divisors

The number 1728 has 28 divisors, written as τ(1728) = 28 in number theory.

Sum of Divisors

σ(1728) = 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 16 + 18 + 24 + 27 + 32 + 36 + 48 + 54 + 64 + 72 + 96 + 108 + 144 + 192 + 216 + 288 + 432 + 576 + 864 + 1728 = 5080

Prime Factorization of 1728

See the full prime factorization calculator →

Properties of 1728

• 1728 is composite.
• 1728 is not a perfect square.
• Number of divisors: 28.
• Sum of divisors: 5080.

Common Divisors with Another Number?

Looking for the divisors that 1728 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 1728

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √1728 ≈ 41.57. If i divides 1728, then both i and 1728/i are divisors.

1. 1 divides 1728 (1728 ÷ 1 = 1728) → pair (1, 1728)
2. 2 divides 1728 (1728 ÷ 2 = 864) → pair (2, 864)
3. 3 divides 1728 (1728 ÷ 3 = 576) → pair (3, 576)
4. 4 divides 1728 (1728 ÷ 4 = 432) → pair (4, 432)
5. 6 divides 1728 (1728 ÷ 6 = 288) → pair (6, 288)
6. 8 divides 1728 (1728 ÷ 8 = 216) → pair (8, 216)
7. 9 divides 1728 (1728 ÷ 9 = 192) → pair (9, 192)
8. 12 divides 1728 (1728 ÷ 12 = 144) → pair (12, 144)
9. 16 divides 1728 (1728 ÷ 16 = 108) → pair (16, 108)
10. 18 divides 1728 (1728 ÷ 18 = 96) → pair (18, 96)
11. 24 divides 1728 (1728 ÷ 24 = 72) → pair (24, 72)
12. 27 divides 1728 (1728 ÷ 27 = 64) → pair (27, 64)
13. 32 divides 1728 (1728 ÷ 32 = 54) → pair (32, 54)
14. 36 divides 1728 (1728 ÷ 36 = 48) → pair (36, 48)
15. Collect all unique values: {1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 144, 192, 216, 288, 432, 576, 864, 1728} — total 28 divisors.
16. Sum: 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 16 + 18 + 24 + 27 + 32 + 36 + 48 + 54 + 64 + 72 + 96 + 108 + 144 + 192 + 216 + 288 + 432 + 576 + 864 + 1728 = 5080.

Nearby Examples

Related Operations for 1728

• Multiples of 1728 — "outward" complement; M is a multiple of 1728 ⇔ 1728 is a divisor of M
• 1728 Prime Factorization — decompose into prime building blocks
• Find GCF of 1728 and another number
• Find LCM of 1728 and another number
• Is 1728 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)

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