Divisors of 560: All 20 Factors
Quick Answer
560 has 20 divisors (factors): 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280, 560.
Sum: 1488.
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 560
The number 560 has 20 divisors:
1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280, 560
Divisor Pairs of 560
Each pair multiplies to 560:
| Factor 1 | × | Factor 2 | = | Product |
|---|---|---|---|---|
| 1 | × | 560 | = | 560 |
| 2 | × | 280 | = | 560 |
| 4 | × | 140 | = | 560 |
| 5 | × | 112 | = | 560 |
| 7 | × | 80 | = | 560 |
| 8 | × | 70 | = | 560 |
| 10 | × | 56 | = | 560 |
| 14 | × | 40 | = | 560 |
| 16 | × | 35 | = | 560 |
| 20 | × | 28 | = | 560 |
Number of Divisors
The number 560 has 20 divisors, written as τ(560) = 20 in number theory.
Sum of Divisors
σ(560) = 1 + 2 + 4 + 5 + 7 + 8 + 10 + 14 + 16 + 20 + 28 + 35 + 40 + 56 + 70 + 80 + 112 + 140 + 280 + 560 = 1488
Prime Factorization of 560
Properties of 560
- 560 is composite.
- 560 is not a perfect square.
- Number of divisors: 20.
- Sum of divisors: 1488.
Common Divisors with Another Number?
Looking for the divisors that 560 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 560
An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √560 ≈ 23.66. If i divides 560, then both i and 560/i are divisors.
- 1 divides 560 (560 ÷ 1 = 560) → pair (1, 560)
- 2 divides 560 (560 ÷ 2 = 280) → pair (2, 280)
- 4 divides 560 (560 ÷ 4 = 140) → pair (4, 140)
- 5 divides 560 (560 ÷ 5 = 112) → pair (5, 112)
- 7 divides 560 (560 ÷ 7 = 80) → pair (7, 80)
- 8 divides 560 (560 ÷ 8 = 70) → pair (8, 70)
- 10 divides 560 (560 ÷ 10 = 56) → pair (10, 56)
- 14 divides 560 (560 ÷ 14 = 40) → pair (14, 40)
- 16 divides 560 (560 ÷ 16 = 35) → pair (16, 35)
- 20 divides 560 (560 ÷ 20 = 28) → pair (20, 28)
- Collect all unique values: {1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280, 560} — total 20 divisors.
- Sum: 1 + 2 + 4 + 5 + 7 + 8 + 10 + 14 + 16 + 20 + 28 + 35 + 40 + 56 + 70 + 80 + 112 + 140 + 280 + 560 = 1488.
Nearby Examples
Related Operations for 560
- Multiples of 560 — "outward" complement; M is a multiple of 560 ⇔ 560 is a divisor of M
- 560 Prime Factorization — decompose into prime building blocks
- Find GCF of 560 and another number
- Find LCM of 560 and another number
- Is 560 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