Divisors of 10000: All 25 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 10000

The number 10000 has 25 divisors:

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

Divisor Pairs of 10000

Each pair multiplies to 10000:

Note: the last pair has identical factors (100 × 100) because 10000 is a perfect square.

Number of Divisors

The number 10000 has 25 divisors, written as τ(10000) = 25 in number theory.

⚡ Notice: 10000 has an odd number of divisors — this means 10000 is a perfect square (√10000 = 100).

Sum of Divisors

σ(10000) = 1 + 2 + 4 + 5 + 8 + 10 + 16 + 20 + 25 + 40 + 50 + 80 + 100 + 125 + 200 + 250 + 400 + 500 + 625 + 1000 + 1250 + 2000 + 2500 + 5000 + 10000 = 24211

Prime Factorization of 10000

See the full prime factorization calculator →

Properties of 10000

• 10000 is composite.
• 10000 is a perfect square (√10000 = 100).
• Number of divisors: 25.
• Sum of divisors: 24211.

Common Divisors with Another Number?

Looking for the divisors that 10000 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 10000

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √10000 ≈ 100.00. If i divides 10000, then both i and 10000/i are divisors.

1. 1 divides 10000 (10000 ÷ 1 = 10000) → pair (1, 10000)
2. 2 divides 10000 (10000 ÷ 2 = 5000) → pair (2, 5000)
3. 4 divides 10000 (10000 ÷ 4 = 2500) → pair (4, 2500)
4. 5 divides 10000 (10000 ÷ 5 = 2000) → pair (5, 2000)
5. 8 divides 10000 (10000 ÷ 8 = 1250) → pair (8, 1250)
6. 10 divides 10000 (10000 ÷ 10 = 1000) → pair (10, 1000)
7. 16 divides 10000 (10000 ÷ 16 = 625) → pair (16, 625)
8. 20 divides 10000 (10000 ÷ 20 = 500) → pair (20, 500)
9. 25 divides 10000 (10000 ÷ 25 = 400) → pair (25, 400)
10. 40 divides 10000 (10000 ÷ 40 = 250) → pair (40, 250)
11. 50 divides 10000 (10000 ÷ 50 = 200) → pair (50, 200)
12. 80 divides 10000 (10000 ÷ 80 = 125) → pair (80, 125)
13. 100 divides 10000 (10000 ÷ 100 = 100) → pair (100, 100)
14. Collect all unique values: {1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 625, 1000, 1250, 2000, 2500, 5000, 10000} — total 25 divisors.
15. Sum: 1 + 2 + 4 + 5 + 8 + 10 + 16 + 20 + 25 + 40 + 50 + 80 + 100 + 125 + 200 + 250 + 400 + 500 + 625 + 1000 + 1250 + 2000 + 2500 + 5000 + 10000 = 24211.

Nearby Examples

Related Operations for 10000

• Multiples of 10000 — "outward" complement; M is a multiple of 10000 ⇔ 10000 is a divisor of M
• 10000 Prime Factorization — decompose into prime building blocks
• Find GCF of 10000 and another number
• Find LCM of 10000 and another number
• Is 10000 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: