Divisors of 20000: All 30 Factors

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 20000

The number 20000 has 30 divisors:

1,  2,  4,  5,  8,  10,  16,  20,  25,  32,  40,  50,  80,  100,  125,  160,  200,  250,  400,  500,  625,  800,  1000,  1250,  2000,  2500,  4000,  5000,  10000,  20000

Divisor Pairs of 20000

Each pair multiplies to 20000:

Number of Divisors

The number 20000 has 30 divisors, written as τ(20000) = 30 in number theory.

Sum of Divisors

σ(20000) = 1 + 2 + 4 + 5 + 8 + 10 + 16 + 20 + 25 + 32 + 40 + 50 + 80 + 100 + 125 + 160 + 200 + 250 + 400 + 500 + 625 + 800 + 1000 + 1250 + 2000 + 2500 + 4000 + 5000 + 10000 + 20000 = 49203

Prime Factorization of 20000

See the full prime factorization calculator →

Properties of 20000

• 20000 is composite.
• 20000 is not a perfect square.
• Number of divisors: 30.
• Sum of divisors: 49203.

Common Divisors with Another Number?

Looking for the divisors that 20000 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 20000

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √20000 ≈ 141.42. If i divides 20000, then both i and 20000/i are divisors.

1. 1 divides 20000 (20000 ÷ 1 = 20000) → pair (1, 20000)
2. 2 divides 20000 (20000 ÷ 2 = 10000) → pair (2, 10000)
3. 4 divides 20000 (20000 ÷ 4 = 5000) → pair (4, 5000)
4. 5 divides 20000 (20000 ÷ 5 = 4000) → pair (5, 4000)
5. 8 divides 20000 (20000 ÷ 8 = 2500) → pair (8, 2500)
6. 10 divides 20000 (20000 ÷ 10 = 2000) → pair (10, 2000)
7. 16 divides 20000 (20000 ÷ 16 = 1250) → pair (16, 1250)
8. 20 divides 20000 (20000 ÷ 20 = 1000) → pair (20, 1000)
9. 25 divides 20000 (20000 ÷ 25 = 800) → pair (25, 800)
10. 32 divides 20000 (20000 ÷ 32 = 625) → pair (32, 625)
11. 40 divides 20000 (20000 ÷ 40 = 500) → pair (40, 500)
12. 50 divides 20000 (20000 ÷ 50 = 400) → pair (50, 400)
13. 80 divides 20000 (20000 ÷ 80 = 250) → pair (80, 250)
14. 100 divides 20000 (20000 ÷ 100 = 200) → pair (100, 200)
15. 125 divides 20000 (20000 ÷ 125 = 160) → pair (125, 160)
16. Collect all unique values: {1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 125, 160, 200, 250, 400, 500, 625, 800, 1000, 1250, 2000, 2500, 4000, 5000, 10000, 20000} — total 30 divisors.
17. Sum: 1 + 2 + 4 + 5 + 8 + 10 + 16 + 20 + 25 + 32 + 40 + 50 + 80 + 100 + 125 + 160 + 200 + 250 + 400 + 500 + 625 + 800 + 1000 + 1250 + 2000 + 2500 + 4000 + 5000 + 10000 + 20000 = 49203.

Nearby Examples

Related Operations for 20000

• Multiples of a Number — "outward" complement of divisors
• 20000 Prime Factorization — decompose into prime building blocks
• Find GCF of 20000 and another number
• Find LCM of 20000 and another number
• Is 20000 a perfect square? (odd divisor count ⇔ yes)

See also our tables of divisors:

• Table of all divisors from 1 to 100
• Table of all divisors from 1 to 500
• Table of all divisors from 1 to 1,000
• Table of all divisors from 1 to 10,000

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.

References

• [1] Divisor (Wikipedia)
• [2] Divisor function (Wikipedia)
• [3] Divisor (Wolfram MathWorld)

Divisors Calculation Examples

Find all divisors of these numbers: