Is 10400 a prime number?

No. 10400 is composite — it has more than 2 divisors (it has 36).

Divisors of 10400: All 36 Factors

Q: What are the divisors of 10400?

The divisors (factors) of 10400 are 1, 2, 4, 5, 8, 10, 13, 16, 20, 25, 26, 32, 40, 50, 52, 65, 80, 100, 104, 130, 160, 200, 208, 260, 325, 400, 416, 520, 650, 800, 1040, 1300, 2080, 2600, 5200, 10400.

Q: What is the sum of the divisors of 10400?

The sum is 1 + 2 + 4 + 5 + 8 + 10 + 13 + 16 + 20 + 25 + 26 + 32 + 40 + 50 + 52 + 65 + 80 + 100 + 104 + 130 + 160 + 200 + 208 + 260 + 325 + 400 + 416 + 520 + 650 + 800 + 1040 + 1300 + 2080 + 2600 + 5200 + 10400 = 27342.

Quick Answer

10400 has 36 divisors (factors): 1, 2, 4, 5, 8, 10, 13, 16, 20, 25, 26, 32, 40, 50, 52, 65, 80, 100, 104, 130, 160, 200, 208, 260, 325, 400, 416, 520, 650, 800, 1040, 1300, 2080, 2600, 5200, 10400.

Sum: 27342.

Divisors (Factors) Calculator

Divisors Multiples Prime Factoriz. GCF LCM

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 10400

The number 10400 has 36 divisors:

1, 2, 4, 5, 8, 10, 13, 16, 20, 25, 26, 32, 40, 50, 52, 65, 80, 100, 104, 130, 160, 200, 208, 260, 325, 400, 416, 520, 650, 800, 1040, 1300, 2080, 2600, 5200, 10400

Divisor Pairs of 10400

Each pair multiplies to 10400:

Factor 1	×	Factor 2	=	Product
1	×	10400	=	10400
2	×	5200	=	10400
4	×	2600	=	10400
5	×	2080	=	10400
8	×	1300	=	10400
10	×	1040	=	10400
13	×	800	=	10400
16	×	650	=	10400
20	×	520	=	10400
25	×	416	=	10400
26	×	400	=	10400
32	×	325	=	10400
40	×	260	=	10400
50	×	208	=	10400
52	×	200	=	10400
65	×	160	=	10400
80	×	130	=	10400
100	×	104	=	10400

Number of Divisors

The number 10400 has 36 divisors, written as τ(10400) = 36 in number theory.

Sum of Divisors

σ(10400) = 1 + 2 + 4 + 5 + 8 + 10 + 13 + 16 + 20 + 25 + 26 + 32 + 40 + 50 + 52 + 65 + 80 + 100 + 104 + 130 + 160 + 200 + 208 + 260 + 325 + 400 + 416 + 520 + 650 + 800 + 1040 + 1300 + 2080 + 2600 + 5200 + 10400 = 27342

Prime Factorization of 10400

See the full prime factorization calculator →

Properties of 10400

10400 is composite.
10400 is not a perfect square.
Number of divisors: 36.
Sum of divisors: 27342.

Common Divisors with Another Number?

Looking for the divisors that 10400 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 10400

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √10400 ≈ 101.98. If i divides 10400, then both i and 10400/i are divisors.

1 divides 10400 (10400 ÷ 1 = 10400) → pair (1, 10400)
2 divides 10400 (10400 ÷ 2 = 5200) → pair (2, 5200)
4 divides 10400 (10400 ÷ 4 = 2600) → pair (4, 2600)
5 divides 10400 (10400 ÷ 5 = 2080) → pair (5, 2080)
8 divides 10400 (10400 ÷ 8 = 1300) → pair (8, 1300)
10 divides 10400 (10400 ÷ 10 = 1040) → pair (10, 1040)
13 divides 10400 (10400 ÷ 13 = 800) → pair (13, 800)
16 divides 10400 (10400 ÷ 16 = 650) → pair (16, 650)
20 divides 10400 (10400 ÷ 20 = 520) → pair (20, 520)
25 divides 10400 (10400 ÷ 25 = 416) → pair (25, 416)
26 divides 10400 (10400 ÷ 26 = 400) → pair (26, 400)
32 divides 10400 (10400 ÷ 32 = 325) → pair (32, 325)
40 divides 10400 (10400 ÷ 40 = 260) → pair (40, 260)
50 divides 10400 (10400 ÷ 50 = 208) → pair (50, 208)
52 divides 10400 (10400 ÷ 52 = 200) → pair (52, 200)
65 divides 10400 (10400 ÷ 65 = 160) → pair (65, 160)
80 divides 10400 (10400 ÷ 80 = 130) → pair (80, 130)
100 divides 10400 (10400 ÷ 100 = 104) → pair (100, 104)
Collect all unique values: {1, 2, 4, 5, 8, 10, 13, 16, 20, 25, 26, 32, 40, 50, 52, 65, 80, 100, 104, 130, 160, 200, 208, 260, 325, 400, 416, 520, 650, 800, 1040, 1300, 2080, 2600, 5200, 10400} — total 36 divisors.
Sum: 1 + 2 + 4 + 5 + 8 + 10 + 13 + 16 + 20 + 25 + 26 + 32 + 40 + 50 + 52 + 65 + 80 + 100 + 104 + 130 + 160 + 200 + 208 + 260 + 325 + 400 + 416 + 520 + 650 + 800 + 1040 + 1300 + 2080 + 2600 + 5200 + 10400 = 27342.

Nearby Examples

n	divisors count	sum σ(n)
360	24	1170
240	20	744
180	18	546
144	15	403
120	16	360
100	9	217
90	12	234
84	12	224

Related Operations for 10400

Multiples of a Number — "outward" complement of divisors
10400 Prime Factorization — decompose into prime building blocks
Find GCF of 10400 and another number
Find LCM of 10400 and another number
Is 10400 a perfect square? (odd divisor count ⇔ yes)

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

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