Divisors of 441: All 9 Factors
Quick Answer
441 has 9 divisors (factors): 1, 3, 7, 9, 21, 49, 63, 147, 441.
Sum: 741. 441 is a perfect square (√441 = 21).
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 441
The number 441 has 9 divisors:
1, 3, 7, 9, 21, 49, 63, 147, 441
Divisor Pairs of 441
Each pair multiplies to 441:
| Factor 1 | × | Factor 2 | = | Product |
|---|---|---|---|---|
| 1 | × | 441 | = | 441 |
| 3 | × | 147 | = | 441 |
| 7 | × | 63 | = | 441 |
| 9 | × | 49 | = | 441 |
| 21 | × | 21 | = | 441 |
Note: the last pair has identical factors (21 × 21) because 441 is a perfect square.
Number of Divisors
The number 441 has 9 divisors, written as τ(441) = 9 in number theory.
⚡ Notice: 441 has an odd number of divisors — this means 441 is a perfect square (√441 = 21).
Sum of Divisors
σ(441) = 1 + 3 + 7 + 9 + 21 + 49 + 63 + 147 + 441 = 741
Prime Factorization of 441
Properties of 441
- 441 is composite.
- 441 is a perfect square (√441 = 21).
- Number of divisors: 9.
- Sum of divisors: 741.
Common Divisors with Another Number?
Looking for the divisors that 441 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 441
An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √441 ≈ 21.00. If i divides 441, then both i and 441/i are divisors.
- 1 divides 441 (441 ÷ 1 = 441) → pair (1, 441)
- 3 divides 441 (441 ÷ 3 = 147) → pair (3, 147)
- 7 divides 441 (441 ÷ 7 = 63) → pair (7, 63)
- 9 divides 441 (441 ÷ 9 = 49) → pair (9, 49)
- 21 divides 441 (441 ÷ 21 = 21) → pair (21, 21)
- Collect all unique values: {1, 3, 7, 9, 21, 49, 63, 147, 441} — total 9 divisors.
- Sum: 1 + 3 + 7 + 9 + 21 + 49 + 63 + 147 + 441 = 741.
Nearby Examples
Related Operations for 441
- Multiples of 441 — "outward" complement; M is a multiple of 441 ⇔ 441 is a divisor of M
- 441 Prime Factorization — decompose into prime building blocks
- Find GCF of 441 and another number
- Find LCM of 441 and another number
- Is 441 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