Divisors of 506: All 8 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 506

The number 506 has 8 divisors:

1,  2,  11,  22,  23,  46,  253,  506

Divisor Pairs of 506

Each pair multiplies to 506:

Number of Divisors

The number 506 has 8 divisors, written as τ(506) = 8 in number theory.

Sum of Divisors

σ(506) = 1 + 2 + 11 + 22 + 23 + 46 + 253 + 506 = 864

Prime Factorization of 506

See the full prime factorization calculator →

Properties of 506

• 506 is composite.
• 506 is not a perfect square.
• Number of divisors: 8.
• Sum of divisors: 864.

Common Divisors with Another Number?

Looking for the divisors that 506 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 506

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √506 ≈ 22.49. If i divides 506, then both i and 506/i are divisors.

1. 1 divides 506 (506 ÷ 1 = 506) → pair (1, 506)
2. 2 divides 506 (506 ÷ 2 = 253) → pair (2, 253)
3. 11 divides 506 (506 ÷ 11 = 46) → pair (11, 46)
4. 22 divides 506 (506 ÷ 22 = 23) → pair (22, 23)
5. Collect all unique values: {1, 2, 11, 22, 23, 46, 253, 506} — total 8 divisors.
6. Sum: 1 + 2 + 11 + 22 + 23 + 46 + 253 + 506 = 864.

Nearby Examples

Related Operations for 506

• Multiples of 506 — "outward" complement; M is a multiple of 506 ⇔ 506 is a divisor of M
• 506 Prime Factorization — decompose into prime building blocks
• Find GCF of 506 and another number
• Find LCM of 506 and another number
• Is 506 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

Find all divisors of these numbers: