Divisors of 52: All 6 Factors
Quick Answer
52 has 6 divisors (factors): 1, 2, 4, 13, 26, 52.
Sum: 98.
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 52
The number 52 has 6 divisors:
1, 2, 4, 13, 26, 52
Divisor Pairs of 52
Each pair multiplies to 52:
| Factor 1 | × | Factor 2 | = | Product |
|---|---|---|---|---|
| 1 | × | 52 | = | 52 |
| 2 | × | 26 | = | 52 |
| 4 | × | 13 | = | 52 |
Number of Divisors
The number 52 has 6 divisors, written as τ(52) = 6 in number theory.
Sum of Divisors
σ(52) = 1 + 2 + 4 + 13 + 26 + 52 = 98
Prime Factorization of 52
Properties of 52
- 52 is composite.
- 52 is not a perfect square.
- Number of divisors: 6.
- Sum of divisors: 98.
Common Divisors with Another Number?
Looking for the divisors that 52 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 52
An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √52 ≈ 7.21. If i divides 52, then both i and 52/i are divisors.
- 1 divides 52 (52 ÷ 1 = 52) → pair (1, 52)
- 2 divides 52 (52 ÷ 2 = 26) → pair (2, 26)
- 4 divides 52 (52 ÷ 4 = 13) → pair (4, 13)
- Collect all unique values: {1, 2, 4, 13, 26, 52} — total 6 divisors.
- Sum: 1 + 2 + 4 + 13 + 26 + 52 = 98.
Related Operations for 52
- Multiples of 52 — "outward" complement; M is a multiple of 52 ⇔ 52 is a divisor of M
- 52 Prime Factorization — decompose into prime building blocks
- Find GCF of 52 and another number
- Find LCM of 52 and another number
- Is 52 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