Divisors of 693: All 12 Factors
Quick Answer
693 has 12 divisors (factors): 1, 3, 7, 9, 11, 21, 33, 63, 77, 99, 231, 693.
Sum: 1248.
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 693
The number 693 has 12 divisors:
1, 3, 7, 9, 11, 21, 33, 63, 77, 99, 231, 693
Divisor Pairs of 693
Each pair multiplies to 693:
| Factor 1 | × | Factor 2 | = | Product |
|---|---|---|---|---|
| 1 | × | 693 | = | 693 |
| 3 | × | 231 | = | 693 |
| 7 | × | 99 | = | 693 |
| 9 | × | 77 | = | 693 |
| 11 | × | 63 | = | 693 |
| 21 | × | 33 | = | 693 |
Number of Divisors
The number 693 has 12 divisors, written as τ(693) = 12 in number theory.
Sum of Divisors
σ(693) = 1 + 3 + 7 + 9 + 11 + 21 + 33 + 63 + 77 + 99 + 231 + 693 = 1248
Prime Factorization of 693
Properties of 693
- 693 is composite.
- 693 is not a perfect square.
- Number of divisors: 12.
- Sum of divisors: 1248.
Common Divisors with Another Number?
Looking for the divisors that 693 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 693
An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √693 ≈ 26.32. If i divides 693, then both i and 693/i are divisors.
- 1 divides 693 (693 ÷ 1 = 693) → pair (1, 693)
- 3 divides 693 (693 ÷ 3 = 231) → pair (3, 231)
- 7 divides 693 (693 ÷ 7 = 99) → pair (7, 99)
- 9 divides 693 (693 ÷ 9 = 77) → pair (9, 77)
- 11 divides 693 (693 ÷ 11 = 63) → pair (11, 63)
- 21 divides 693 (693 ÷ 21 = 33) → pair (21, 33)
- Collect all unique values: {1, 3, 7, 9, 11, 21, 33, 63, 77, 99, 231, 693} — total 12 divisors.
- Sum: 1 + 3 + 7 + 9 + 11 + 21 + 33 + 63 + 77 + 99 + 231 + 693 = 1248.
Nearby Examples
Related Operations for 693
- Multiples of 693 — "outward" complement; M is a multiple of 693 ⇔ 693 is a divisor of M
- 693 Prime Factorization — decompose into prime building blocks
- Find GCF of 693 and another number
- Find LCM of 693 and another number
- Is 693 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