Divisors of 431: 2 Factors (Prime)

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 431

431 is prime, so it has exactly 2 divisors:

1,  431

Divisor Pairs of 431

Each pair multiplies to 431:

Number of Divisors

The number 431 has 2 divisors, written as τ(431) = 2 in number theory.

Sum of Divisors

σ(431) = 1 + 431 = 432

Prime Factorization of 431

See the full prime factorization calculator →

Properties of 431

• 431 is prime.
• 431 is not a perfect square.
• Number of divisors: 2.
• Sum of divisors: 432.

Common Divisors with Another Number?

Looking for the divisors that 431 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 431

1. By definition, a prime number is divisible only by 1 and itself.
2. Check small divisors: we only need to test integers from 2 to √431 ≈ 20.76.
3. None of those divide 431 evenly ⇒ 431 is prime.
4. Divisors of 431: {1, 431}. Sum: 432.

Nearby Examples

Related Operations for 431

• Multiples of 431 — "outward" complement; M is a multiple of 431 ⇔ 431 is a divisor of M
• 431 Prime Factorization — decompose into prime building blocks
• Is 431 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: