Divisors of 40000: All 35 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 40000

The number 40000 has 35 divisors:

1,  2,  4,  5,  8,  10,  16,  20,  25,  32,  40,  50,  64,  80,  100,  125,  160,  200,  250,  320,  400,  500,  625,  800,  1000,  1250,  1600,  2000,  2500,  4000,  5000,  8000,  10000,  20000,  40000

Divisor Pairs of 40000

Each pair multiplies to 40000:

Note: the last pair has identical factors (200 × 200) because 40000 is a perfect square.

Number of Divisors

The number 40000 has 35 divisors, written as τ(40000) = 35 in number theory.

⚡ Notice: 40000 has an odd number of divisors — this means 40000 is a perfect square (√40000 = 200).

Sum of Divisors

σ(40000) = 1 + 2 + 4 + 5 + 8 + 10 + 16 + 20 + 25 + 32 + 40 + 50 + 64 + 80 + 100 + 125 + 160 + 200 + 250 + 320 + 400 + 500 + 625 + 800 + 1000 + 1250 + 1600 + 2000 + 2500 + 4000 + 5000 + 8000 + 10000 + 20000 + 40000 = 99187

Prime Factorization of 40000

See the full prime factorization calculator →

Properties of 40000

• 40000 is composite.
• 40000 is a perfect square (√40000 = 200).
• Number of divisors: 35.
• Sum of divisors: 99187.

Common Divisors with Another Number?

Looking for the divisors that 40000 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 40000

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √40000 ≈ 200.00. If i divides 40000, then both i and 40000/i are divisors.

1. 1 divides 40000 (40000 ÷ 1 = 40000) → pair (1, 40000)
2. 2 divides 40000 (40000 ÷ 2 = 20000) → pair (2, 20000)
3. 4 divides 40000 (40000 ÷ 4 = 10000) → pair (4, 10000)
4. 5 divides 40000 (40000 ÷ 5 = 8000) → pair (5, 8000)
5. 8 divides 40000 (40000 ÷ 8 = 5000) → pair (8, 5000)
6. 10 divides 40000 (40000 ÷ 10 = 4000) → pair (10, 4000)
7. 16 divides 40000 (40000 ÷ 16 = 2500) → pair (16, 2500)
8. 20 divides 40000 (40000 ÷ 20 = 2000) → pair (20, 2000)
9. 25 divides 40000 (40000 ÷ 25 = 1600) → pair (25, 1600)
10. 32 divides 40000 (40000 ÷ 32 = 1250) → pair (32, 1250)
11. 40 divides 40000 (40000 ÷ 40 = 1000) → pair (40, 1000)
12. 50 divides 40000 (40000 ÷ 50 = 800) → pair (50, 800)
13. 64 divides 40000 (40000 ÷ 64 = 625) → pair (64, 625)
14. 80 divides 40000 (40000 ÷ 80 = 500) → pair (80, 500)
15. 100 divides 40000 (40000 ÷ 100 = 400) → pair (100, 400)
16. 125 divides 40000 (40000 ÷ 125 = 320) → pair (125, 320)
17. 160 divides 40000 (40000 ÷ 160 = 250) → pair (160, 250)
18. 200 divides 40000 (40000 ÷ 200 = 200) → pair (200, 200)
19. Collect all unique values: {1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125, 160, 200, 250, 320, 400, 500, 625, 800, 1000, 1250, 1600, 2000, 2500, 4000, 5000, 8000, 10000, 20000, 40000} — total 35 divisors.
20. Sum: 1 + 2 + 4 + 5 + 8 + 10 + 16 + 20 + 25 + 32 + 40 + 50 + 64 + 80 + 100 + 125 + 160 + 200 + 250 + 320 + 400 + 500 + 625 + 800 + 1000 + 1250 + 1600 + 2000 + 2500 + 4000 + 5000 + 8000 + 10000 + 20000 + 40000 = 99187.

Nearby Examples

Related Operations for 40000

• Multiples of a Number — "outward" complement of divisors
• 40000 Prime Factorization — decompose into prime building blocks
• Find GCF of 40000 and another number
• Find LCM of 40000 and another number
• Is 40000 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: