Divisors of 361: 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 361

The number 361 has 3 divisors:

1,  19,  361

Divisor Pairs of 361

Each pair multiplies to 361:

Note: the last pair has identical factors (19 × 19) because 361 is a perfect square.

Number of Divisors

The number 361 has 3 divisors, written as τ(361) = 3 in number theory.

⚡ Notice: 361 has an odd number of divisors — this means 361 is a perfect square (√361 = 19).

Sum of Divisors

σ(361) = 1 + 19 + 361 = 381

Prime Factorization of 361

See the full prime factorization calculator →

Properties of 361

• 361 is composite.
• 361 is a perfect square (√361 = 19).
• Number of divisors: 3.
• Sum of divisors: 381.

Common Divisors with Another Number?

Looking for the divisors that 361 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 361

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √361 ≈ 19.00. If i divides 361, then both i and 361/i are divisors.

1. 1 divides 361 (361 ÷ 1 = 361) → pair (1, 361)
2. 19 divides 361 (361 ÷ 19 = 19) → pair (19, 19)
3. Collect all unique values: {1, 19, 361} — total 3 divisors.
4. Sum: 1 + 19 + 361 = 381.

Nearby Examples

Related Operations for 361

• Multiples of 361 — "outward" complement; M is a multiple of 361 ⇔ 361 is a divisor of M
• 361 Prime Factorization — decompose into prime building blocks
• Find GCF of 361 and another number
• Find LCM of 361 and another number
• Is 361 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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