Divisors of 289: All 3 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 289

The number 289 has 3 divisors:

1,  17,  289

Divisor Pairs of 289

Each pair multiplies to 289:

Note: the last pair has identical factors (17 × 17) because 289 is a perfect square.

Number of Divisors

The number 289 has 3 divisors, written as τ(289) = 3 in number theory.

⚡ Notice: 289 has an odd number of divisors — this means 289 is a perfect square (√289 = 17).

Sum of Divisors

σ(289) = 1 + 17 + 289 = 307

Prime Factorization of 289

See the full prime factorization calculator →

Properties of 289

• 289 is composite.
• 289 is a perfect square (√289 = 17).
• Number of divisors: 3.
• Sum of divisors: 307.

Common Divisors with Another Number?

Looking for the divisors that 289 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 289

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √289 ≈ 17.00. If i divides 289, then both i and 289/i are divisors.

1. 1 divides 289 (289 ÷ 1 = 289) → pair (1, 289)
2. 17 divides 289 (289 ÷ 17 = 17) → pair (17, 17)
3. Collect all unique values: {1, 17, 289} — total 3 divisors.
4. Sum: 1 + 17 + 289 = 307.

Nearby Examples

Related Operations for 289

• Multiples of 289 — "outward" complement; M is a multiple of 289 ⇔ 289 is a divisor of M
• 289 Prime Factorization — decompose into prime building blocks
• Find GCF of 289 and another number
• Find LCM of 289 and another number
• Is 289 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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