Is 42400 a prime number?

No. 42400 is composite — it has more than 2 divisors (it has 36).

Divisors of 42400: All 36 Factors

Q: What are the divisors of 42400?

The divisors (factors) of 42400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 53, 80, 100, 106, 160, 200, 212, 265, 400, 424, 530, 800, 848, 1060, 1325, 1696, 2120, 2650, 4240, 5300, 8480, 10600, 21200, 42400.

Q: What is the sum of the divisors of 42400?

The sum is 1 + 2 + 4 + 5 + 8 + 10 + 16 + 20 + 25 + 32 + 40 + 50 + 53 + 80 + 100 + 106 + 160 + 200 + 212 + 265 + 400 + 424 + 530 + 800 + 848 + 1060 + 1325 + 1696 + 2120 + 2650 + 4240 + 5300 + 8480 + 10600 + 21200 + 42400 = 105462.

Quick Answer

42400 has 36 divisors (factors): 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 53, 80, 100, 106, 160, 200, 212, 265, 400, 424, 530, 800, 848, 1060, 1325, 1696, 2120, 2650, 4240, 5300, 8480, 10600, 21200, 42400.

Sum: 105462.

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 42400

The number 42400 has 36 divisors:

1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 53, 80, 100, 106, 160, 200, 212, 265, 400, 424, 530, 800, 848, 1060, 1325, 1696, 2120, 2650, 4240, 5300, 8480, 10600, 21200, 42400

Divisor Pairs of 42400

Each pair multiplies to 42400:

Factor 1	×	Factor 2	=	Product
1	×	42400	=	42400
2	×	21200	=	42400
4	×	10600	=	42400
5	×	8480	=	42400
8	×	5300	=	42400
10	×	4240	=	42400
16	×	2650	=	42400
20	×	2120	=	42400
25	×	1696	=	42400
32	×	1325	=	42400
40	×	1060	=	42400
50	×	848	=	42400
53	×	800	=	42400
80	×	530	=	42400
100	×	424	=	42400
106	×	400	=	42400
160	×	265	=	42400
200	×	212	=	42400

Number of Divisors

The number 42400 has 36 divisors, written as τ(42400) = 36 in number theory.

Sum of Divisors

σ(42400) = 1 + 2 + 4 + 5 + 8 + 10 + 16 + 20 + 25 + 32 + 40 + 50 + 53 + 80 + 100 + 106 + 160 + 200 + 212 + 265 + 400 + 424 + 530 + 800 + 848 + 1060 + 1325 + 1696 + 2120 + 2650 + 4240 + 5300 + 8480 + 10600 + 21200 + 42400 = 105462

Prime Factorization of 42400

See the full prime factorization calculator →

Properties of 42400

42400 is composite.
42400 is not a perfect square.
Number of divisors: 36.
Sum of divisors: 105462.

Common Divisors with Another Number?

Looking for the divisors that 42400 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 42400

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √42400 ≈ 205.91. If i divides 42400, then both i and 42400/i are divisors.

1 divides 42400 (42400 ÷ 1 = 42400) → pair (1, 42400)
2 divides 42400 (42400 ÷ 2 = 21200) → pair (2, 21200)
4 divides 42400 (42400 ÷ 4 = 10600) → pair (4, 10600)
5 divides 42400 (42400 ÷ 5 = 8480) → pair (5, 8480)
8 divides 42400 (42400 ÷ 8 = 5300) → pair (8, 5300)
10 divides 42400 (42400 ÷ 10 = 4240) → pair (10, 4240)
16 divides 42400 (42400 ÷ 16 = 2650) → pair (16, 2650)
20 divides 42400 (42400 ÷ 20 = 2120) → pair (20, 2120)
25 divides 42400 (42400 ÷ 25 = 1696) → pair (25, 1696)
32 divides 42400 (42400 ÷ 32 = 1325) → pair (32, 1325)
40 divides 42400 (42400 ÷ 40 = 1060) → pair (40, 1060)
50 divides 42400 (42400 ÷ 50 = 848) → pair (50, 848)
53 divides 42400 (42400 ÷ 53 = 800) → pair (53, 800)
80 divides 42400 (42400 ÷ 80 = 530) → pair (80, 530)
100 divides 42400 (42400 ÷ 100 = 424) → pair (100, 424)
106 divides 42400 (42400 ÷ 106 = 400) → pair (106, 400)
160 divides 42400 (42400 ÷ 160 = 265) → pair (160, 265)
200 divides 42400 (42400 ÷ 200 = 212) → pair (200, 212)
Collect all unique values: {1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 53, 80, 100, 106, 160, 200, 212, 265, 400, 424, 530, 800, 848, 1060, 1325, 1696, 2120, 2650, 4240, 5300, 8480, 10600, 21200, 42400} — total 36 divisors.
Sum: 1 + 2 + 4 + 5 + 8 + 10 + 16 + 20 + 25 + 32 + 40 + 50 + 53 + 80 + 100 + 106 + 160 + 200 + 212 + 265 + 400 + 424 + 530 + 800 + 848 + 1060 + 1325 + 1696 + 2120 + 2650 + 4240 + 5300 + 8480 + 10600 + 21200 + 42400 = 105462.

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 42400

Multiples of a Number — "outward" complement of divisors
42400 Prime Factorization — decompose into prime building blocks
Find GCF of 42400 and another number
Find LCM of 42400 and another number
Is 42400 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

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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