Divisors of 21: All 4 Factors
Quick Answer
21 has 4 divisors (factors): 1, 3, 7, 21.
Sum: 32.
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 21
The number 21 has 4 divisors:
1, 3, 7, 21
Divisor Pairs of 21
Each pair multiplies to 21:
| Factor 1 | × | Factor 2 | = | Product |
|---|---|---|---|---|
| 1 | × | 21 | = | 21 |
| 3 | × | 7 | = | 21 |
Number of Divisors
The number 21 has 4 divisors, written as τ(21) = 4 in number theory.
Sum of Divisors
σ(21) = 1 + 3 + 7 + 21 = 32
Prime Factorization of 21
Properties of 21
- 21 is composite.
- 21 is not a perfect square.
- Number of divisors: 4.
- Sum of divisors: 32.
Common Divisors with Another Number?
Looking for the divisors that 21 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 21
An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √21 ≈ 4.58. If i divides 21, then both i and 21/i are divisors.
- 1 divides 21 (21 ÷ 1 = 21) → pair (1, 21)
- 3 divides 21 (21 ÷ 3 = 7) → pair (3, 7)
- Collect all unique values: {1, 3, 7, 21} — total 4 divisors.
- Sum: 1 + 3 + 7 + 21 = 32.
Related Operations for 21
- Multiples of 21 — "outward" complement; M is a multiple of 21 ⇔ 21 is a divisor of M
- 21 Prime Factorization — decompose into prime building blocks
- Find GCF of 21 and another number
- Find LCM of 21 and another number
- Is 21 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