Divisors of 231: 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 231

The number 231 has 8 divisors:

1,  3,  7,  11,  21,  33,  77,  231

Divisor Pairs of 231

Each pair multiplies to 231:

Number of Divisors

The number 231 has 8 divisors, written as τ(231) = 8 in number theory.

Sum of Divisors

σ(231) = 1 + 3 + 7 + 11 + 21 + 33 + 77 + 231 = 384

Prime Factorization of 231

See the full prime factorization calculator →

Properties of 231

• 231 is composite.
• 231 is not a perfect square.
• Number of divisors: 8.
• Sum of divisors: 384.

Common Divisors with Another Number?

Looking for the divisors that 231 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 231

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √231 ≈ 15.20. If i divides 231, then both i and 231/i are divisors.

1. 1 divides 231 (231 ÷ 1 = 231) → pair (1, 231)
2. 3 divides 231 (231 ÷ 3 = 77) → pair (3, 77)
3. 7 divides 231 (231 ÷ 7 = 33) → pair (7, 33)
4. 11 divides 231 (231 ÷ 11 = 21) → pair (11, 21)
5. Collect all unique values: {1, 3, 7, 11, 21, 33, 77, 231} — total 8 divisors.
6. Sum: 1 + 3 + 7 + 11 + 21 + 33 + 77 + 231 = 384.

Nearby Examples

Related Operations for 231

• Multiples of 231 — "outward" complement; M is a multiple of 231 ⇔ 231 is a divisor of M
• 231 Prime Factorization — decompose into prime building blocks
• Find GCF of 231 and another number
• Find LCM of 231 and another number
• Is 231 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: