Divisors of 16384: All 15 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 16384

The number 16384 has 15 divisors:

1,  2,  4,  8,  16,  32,  64,  128,  256,  512,  1024,  2048,  4096,  8192,  16384

Divisor Pairs of 16384

Each pair multiplies to 16384:

Note: the last pair has identical factors (128 × 128) because 16384 is a perfect square.

Number of Divisors

The number 16384 has 15 divisors, written as τ(16384) = 15 in number theory.

⚡ Notice: 16384 has an odd number of divisors — this means 16384 is a perfect square (√16384 = 128).

Sum of Divisors

σ(16384) = 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512 + 1024 + 2048 + 4096 + 8192 + 16384 = 32767

Prime Factorization of 16384

See the full prime factorization calculator →

Properties of 16384

• 16384 is composite.
• 16384 is a perfect square (√16384 = 128).
• Number of divisors: 15.
• Sum of divisors: 32767.

Common Divisors with Another Number?

Looking for the divisors that 16384 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 16384

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √16384 ≈ 128.00. If i divides 16384, then both i and 16384/i are divisors.

1. 1 divides 16384 (16384 ÷ 1 = 16384) → pair (1, 16384)
2. 2 divides 16384 (16384 ÷ 2 = 8192) → pair (2, 8192)
3. 4 divides 16384 (16384 ÷ 4 = 4096) → pair (4, 4096)
4. 8 divides 16384 (16384 ÷ 8 = 2048) → pair (8, 2048)
5. 16 divides 16384 (16384 ÷ 16 = 1024) → pair (16, 1024)
6. 32 divides 16384 (16384 ÷ 32 = 512) → pair (32, 512)
7. 64 divides 16384 (16384 ÷ 64 = 256) → pair (64, 256)
8. 128 divides 16384 (16384 ÷ 128 = 128) → pair (128, 128)
9. Collect all unique values: {1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384} — total 15 divisors.
10. Sum: 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512 + 1024 + 2048 + 4096 + 8192 + 16384 = 32767.

Nearby Examples

Related Operations for 16384

• Multiples of a Number — "outward" complement of divisors
• 16384 Prime Factorization — decompose into prime building blocks
• Find GCF of 16384 and another number
• Find LCM of 16384 and another number
• Is 16384 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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