Divisors of 360: All 24 Factors
Quick Answer
360 has 24 divisors (factors): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360.
Sum: 1170.
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 360
The number 360 has 24 divisors:
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360
Divisor Pairs of 360
Each pair multiplies to 360:
| Factor 1 | × | Factor 2 | = | Product |
|---|---|---|---|---|
| 1 | × | 360 | = | 360 |
| 2 | × | 180 | = | 360 |
| 3 | × | 120 | = | 360 |
| 4 | × | 90 | = | 360 |
| 5 | × | 72 | = | 360 |
| 6 | × | 60 | = | 360 |
| 8 | × | 45 | = | 360 |
| 9 | × | 40 | = | 360 |
| 10 | × | 36 | = | 360 |
| 12 | × | 30 | = | 360 |
| 15 | × | 24 | = | 360 |
| 18 | × | 20 | = | 360 |
Number of Divisors
The number 360 has 24 divisors, written as τ(360) = 24 in number theory.
Sum of Divisors
σ(360) = 1 + 2 + 3 + 4 + 5 + 6 + 8 + 9 + 10 + 12 + 15 + 18 + 20 + 24 + 30 + 36 + 40 + 45 + 60 + 72 + 90 + 120 + 180 + 360 = 1170
Prime Factorization of 360
Properties of 360
- 360 is composite.
- 360 is not a perfect square.
- Number of divisors: 24.
- Sum of divisors: 1170.
Common Divisors with Another Number?
Looking for the divisors that 360 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 360
An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √360 ≈ 18.97. If i divides 360, then both i and 360/i are divisors.
- 1 divides 360 (360 ÷ 1 = 360) → pair (1, 360)
- 2 divides 360 (360 ÷ 2 = 180) → pair (2, 180)
- 3 divides 360 (360 ÷ 3 = 120) → pair (3, 120)
- 4 divides 360 (360 ÷ 4 = 90) → pair (4, 90)
- 5 divides 360 (360 ÷ 5 = 72) → pair (5, 72)
- 6 divides 360 (360 ÷ 6 = 60) → pair (6, 60)
- 8 divides 360 (360 ÷ 8 = 45) → pair (8, 45)
- 9 divides 360 (360 ÷ 9 = 40) → pair (9, 40)
- 10 divides 360 (360 ÷ 10 = 36) → pair (10, 36)
- 12 divides 360 (360 ÷ 12 = 30) → pair (12, 30)
- 15 divides 360 (360 ÷ 15 = 24) → pair (15, 24)
- 18 divides 360 (360 ÷ 18 = 20) → pair (18, 20)
- Collect all unique values: {1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360} — total 24 divisors.
- Sum: 1 + 2 + 3 + 4 + 5 + 6 + 8 + 9 + 10 + 12 + 15 + 18 + 20 + 24 + 30 + 36 + 40 + 45 + 60 + 72 + 90 + 120 + 180 + 360 = 1170.
Nearby Examples
Related Operations for 360
- Multiples of 360 — "outward" complement; M is a multiple of 360 ⇔ 360 is a divisor of M
- 360 Prime Factorization — decompose into prime building blocks
- Find GCF of 360 and another number
- Find LCM of 360 and another number
- Is 360 a perfect square? (odd divisor count ⇔ yes)
See also our tables of divisors:
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.
Divisors Calculation Examples
Find all divisors of these numbers:
Related Calculators
- Multiples of a Number — "outward" complement
- Prime Factorization — product of prime divisors
- Greatest Common Factor (GCF) — largest common divisor of 2+ numbers
- Least Common Multiple (LCM) — smallest common multiple
- Is N a Perfect Square? — odd divisor count check