Divisors of 225: All 9 Factors
Quick Answer
225 has 9 divisors (factors): 1, 3, 5, 9, 15, 25, 45, 75, 225.
Sum: 403. 225 is a perfect square (√225 = 15).
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 225
The number 225 has 9 divisors:
1, 3, 5, 9, 15, 25, 45, 75, 225
Divisor Pairs of 225
Each pair multiplies to 225:
| Factor 1 | × | Factor 2 | = | Product |
|---|---|---|---|---|
| 1 | × | 225 | = | 225 |
| 3 | × | 75 | = | 225 |
| 5 | × | 45 | = | 225 |
| 9 | × | 25 | = | 225 |
| 15 | × | 15 | = | 225 |
Note: the last pair has identical factors (15 × 15) because 225 is a perfect square.
Number of Divisors
The number 225 has 9 divisors, written as τ(225) = 9 in number theory.
⚡ Notice: 225 has an odd number of divisors — this means 225 is a perfect square (√225 = 15).
Sum of Divisors
σ(225) = 1 + 3 + 5 + 9 + 15 + 25 + 45 + 75 + 225 = 403
Prime Factorization of 225
Properties of 225
- 225 is composite.
- 225 is a perfect square (√225 = 15).
- Number of divisors: 9.
- Sum of divisors: 403.
Common Divisors with Another Number?
Looking for the divisors that 225 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 225
An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √225 ≈ 15.00. If i divides 225, then both i and 225/i are divisors.
- 1 divides 225 (225 ÷ 1 = 225) → pair (1, 225)
- 3 divides 225 (225 ÷ 3 = 75) → pair (3, 75)
- 5 divides 225 (225 ÷ 5 = 45) → pair (5, 45)
- 9 divides 225 (225 ÷ 9 = 25) → pair (9, 25)
- 15 divides 225 (225 ÷ 15 = 15) → pair (15, 15)
- Collect all unique values: {1, 3, 5, 9, 15, 25, 45, 75, 225} — total 9 divisors.
- Sum: 1 + 3 + 5 + 9 + 15 + 25 + 45 + 75 + 225 = 403.
Nearby Examples
Related Operations for 225
- Multiples of 225 — "outward" complement; M is a multiple of 225 ⇔ 225 is a divisor of M
- 225 Prime Factorization — decompose into prime building blocks
- Find GCF of 225 and another number
- Find LCM of 225 and another number
- Is 225 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
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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