Divisors of 36400: All 60 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 36400

The number 36400 has 60 divisors:

1,  2,  4,  5,  7,  8,  10,  13,  14,  16,  20,  25,  26,  28,  35,  40,  50,  52,  56,  65,  70,  80,  91,  100,  104,  112,  130,  140,  175,  182,  200,  208,  260,  280,  325,  350,  364,  400,  455,  520,  560,  650,  700,  728,  910,  1040,  1300,  1400,  1456,  1820,  2275,  2600,  2800,  3640,  4550,  5200,  7280,  9100,  18200,  36400

Divisor Pairs of 36400

Each pair multiplies to 36400:

Number of Divisors

The number 36400 has 60 divisors, written as τ(36400) = 60 in number theory.

Sum of Divisors

σ(36400) = 1 + 2 + 4 + 5 + 7 + 8 + 10 + 13 + 14 + 16 + 20 + 25 + 26 + 28 + 35 + 40 + 50 + 52 + 56 + 65 + 70 + 80 + 91 + 100 + 104 + 112 + 130 + 140 + 175 + 182 + 200 + 208 + 260 + 280 + 325 + 350 + 364 + 400 + 455 + 520 + 560 + 650 + 700 + 728 + 910 + 1040 + 1300 + 1400 + 1456 + 1820 + 2275 + 2600 + 2800 + 3640 + 4550 + 5200 + 7280 + 9100 + 18200 + 36400 = 107632

Prime Factorization of 36400

See the full prime factorization calculator →

Properties of 36400

• 36400 is composite.
• 36400 is not a perfect square.
• Number of divisors: 60.
• Sum of divisors: 107632.

Common Divisors with Another Number?

Looking for the divisors that 36400 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 36400

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √36400 ≈ 190.79. If i divides 36400, then both i and 36400/i are divisors.

1. 1 divides 36400 (36400 ÷ 1 = 36400) → pair (1, 36400)
2. 2 divides 36400 (36400 ÷ 2 = 18200) → pair (2, 18200)
3. 4 divides 36400 (36400 ÷ 4 = 9100) → pair (4, 9100)
4. 5 divides 36400 (36400 ÷ 5 = 7280) → pair (5, 7280)
5. 7 divides 36400 (36400 ÷ 7 = 5200) → pair (7, 5200)
6. 8 divides 36400 (36400 ÷ 8 = 4550) → pair (8, 4550)
7. 10 divides 36400 (36400 ÷ 10 = 3640) → pair (10, 3640)
8. 13 divides 36400 (36400 ÷ 13 = 2800) → pair (13, 2800)
9. 14 divides 36400 (36400 ÷ 14 = 2600) → pair (14, 2600)
10. 16 divides 36400 (36400 ÷ 16 = 2275) → pair (16, 2275)
11. 20 divides 36400 (36400 ÷ 20 = 1820) → pair (20, 1820)
12. 25 divides 36400 (36400 ÷ 25 = 1456) → pair (25, 1456)
13. 26 divides 36400 (36400 ÷ 26 = 1400) → pair (26, 1400)
14. 28 divides 36400 (36400 ÷ 28 = 1300) → pair (28, 1300)
15. 35 divides 36400 (36400 ÷ 35 = 1040) → pair (35, 1040)
16. 40 divides 36400 (36400 ÷ 40 = 910) → pair (40, 910)
17. 50 divides 36400 (36400 ÷ 50 = 728) → pair (50, 728)
18. 52 divides 36400 (36400 ÷ 52 = 700) → pair (52, 700)
19. 56 divides 36400 (36400 ÷ 56 = 650) → pair (56, 650)
20. 65 divides 36400 (36400 ÷ 65 = 560) → pair (65, 560)
21. 70 divides 36400 (36400 ÷ 70 = 520) → pair (70, 520)
22. 80 divides 36400 (36400 ÷ 80 = 455) → pair (80, 455)
23. 91 divides 36400 (36400 ÷ 91 = 400) → pair (91, 400)
24. 100 divides 36400 (36400 ÷ 100 = 364) → pair (100, 364)
25. 104 divides 36400 (36400 ÷ 104 = 350) → pair (104, 350)
26. 112 divides 36400 (36400 ÷ 112 = 325) → pair (112, 325)
27. 130 divides 36400 (36400 ÷ 130 = 280) → pair (130, 280)
28. 140 divides 36400 (36400 ÷ 140 = 260) → pair (140, 260)
29. 175 divides 36400 (36400 ÷ 175 = 208) → pair (175, 208)
30. 182 divides 36400 (36400 ÷ 182 = 200) → pair (182, 200)
31. Collect all unique values: {1, 2, 4, 5, 7, 8, 10, 13, 14, 16, 20, 25, 26, 28, 35, 40, 50, 52, 56, 65, 70, 80, 91, 100, 104, 112, 130, 140, 175, 182, 200, 208, 260, 280, 325, 350, 364, 400, 455, 520, 560, 650, 700, 728, 910, 1040, 1300, 1400, 1456, 1820, 2275, 2600, 2800, 3640, 4550, 5200, 7280, 9100, 18200, 36400} — total 60 divisors.
32. Sum: 1 + 2 + 4 + 5 + 7 + 8 + 10 + 13 + 14 + 16 + 20 + 25 + 26 + 28 + 35 + 40 + 50 + 52 + 56 + 65 + 70 + 80 + 91 + 100 + 104 + 112 + 130 + 140 + 175 + 182 + 200 + 208 + 260 + 280 + 325 + 350 + 364 + 400 + 455 + 520 + 560 + 650 + 700 + 728 + 910 + 1040 + 1300 + 1400 + 1456 + 1820 + 2275 + 2600 + 2800 + 3640 + 4550 + 5200 + 7280 + 9100 + 18200 + 36400 = 107632.

Nearby Examples

Related Operations for 36400

• Multiples of a Number — "outward" complement of divisors
• 36400 Prime Factorization — decompose into prime building blocks
• Find GCF of 36400 and another number
• Find LCM of 36400 and another number
• Is 36400 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: