Divisors of 4: All 3 Factors
Quick Answer
4 has 3 divisors (factors): 1, 2, 4.
Sum: 7. 4 is a perfect square (√4 = 2).
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 4
The number 4 has 3 divisors:
1, 2, 4
Divisor Pairs of 4
Each pair multiplies to 4:
| Factor 1 | × | Factor 2 | = | Product |
|---|---|---|---|---|
| 1 | × | 4 | = | 4 |
| 2 | × | 2 | = | 4 |
Note: the last pair has identical factors (2 × 2) because 4 is a perfect square.
Number of Divisors
The number 4 has 3 divisors, written as τ(4) = 3 in number theory.
⚡ Notice: 4 has an odd number of divisors — this means 4 is a perfect square (√4 = 2).
Sum of Divisors
σ(4) = 1 + 2 + 4 = 7
Properties of 4
- 4 is composite.
- 4 is a perfect square (√4 = 2).
- Number of divisors: 3.
- Sum of divisors: 7.
Common Divisors with Another Number?
Looking for the divisors that 4 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 4
An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √4 ≈ 2.00. If i divides 4, then both i and 4/i are divisors.
- 1 divides 4 (4 ÷ 1 = 4) → pair (1, 4)
- 2 divides 4 (4 ÷ 2 = 2) → pair (2, 2)
- Collect all unique values: {1, 2, 4} — total 3 divisors.
- Sum: 1 + 2 + 4 = 7.
Related Operations for 4
- Multiples of 4 — "outward" complement; M is a multiple of 4 ⇔ 4 is a divisor of M
- 4 Prime Factorization — decompose into prime building blocks
- Find GCF of 4 and another number
- Find LCM of 4 and another number
- Is 4 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