Divisors of 1024: All 11 Factors
Quick Answer
1024 has 11 divisors (factors): 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024.
Sum: 2047. 1024 is a perfect square (√1024 = 32).
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 1024
The number 1024 has 11 divisors:
1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024
Divisor Pairs of 1024
Each pair multiplies to 1024:
| Factor 1 | × | Factor 2 | = | Product |
|---|---|---|---|---|
| 1 | × | 1024 | = | 1024 |
| 2 | × | 512 | = | 1024 |
| 4 | × | 256 | = | 1024 |
| 8 | × | 128 | = | 1024 |
| 16 | × | 64 | = | 1024 |
| 32 | × | 32 | = | 1024 |
Note: the last pair has identical factors (32 × 32) because 1024 is a perfect square.
Number of Divisors
The number 1024 has 11 divisors, written as τ(1024) = 11 in number theory.
⚡ Notice: 1024 has an odd number of divisors — this means 1024 is a perfect square (√1024 = 32).
Sum of Divisors
σ(1024) = 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512 + 1024 = 2047
Prime Factorization of 1024
Properties of 1024
- 1024 is composite.
- 1024 is a perfect square (√1024 = 32).
- Number of divisors: 11.
- Sum of divisors: 2047.
Common Divisors with Another Number?
Looking for the divisors that 1024 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 1024
An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √1024 ≈ 32.00. If i divides 1024, then both i and 1024/i are divisors.
- 1 divides 1024 (1024 ÷ 1 = 1024) → pair (1, 1024)
- 2 divides 1024 (1024 ÷ 2 = 512) → pair (2, 512)
- 4 divides 1024 (1024 ÷ 4 = 256) → pair (4, 256)
- 8 divides 1024 (1024 ÷ 8 = 128) → pair (8, 128)
- 16 divides 1024 (1024 ÷ 16 = 64) → pair (16, 64)
- 32 divides 1024 (1024 ÷ 32 = 32) → pair (32, 32)
- Collect all unique values: {1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024} — total 11 divisors.
- Sum: 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512 + 1024 = 2047.
Nearby Examples
Related Operations for 1024
- Multiples of 1024 — "outward" complement; M is a multiple of 1024 ⇔ 1024 is a divisor of M
- 1024 Prime Factorization — decompose into prime building blocks
- Find GCF of 1024 and another number
- Find LCM of 1024 and another number
- Is 1024 a perfect square? (odd divisor count ⇔ yes)
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.
Divisors Calculation Examples
Find all divisors of these numbers:
Related Calculators
- Multiples of a Number — "outward" complement
- Prime Factorization — product of prime divisors
- Greatest Common Factor (GCF) — largest common divisor of 2+ numbers
- Least Common Multiple (LCM) — smallest common multiple
- Is N a Perfect Square? — odd divisor count check