Is 17000 a prime number?

No. 17000 is composite — it has more than 2 divisors (it has 32).

Divisors of 17000: All 32 Factors

Q: What are the divisors of 17000?

The divisors (factors) of 17000 are 1, 2, 4, 5, 8, 10, 17, 20, 25, 34, 40, 50, 68, 85, 100, 125, 136, 170, 200, 250, 340, 425, 500, 680, 850, 1000, 1700, 2125, 3400, 4250, 8500, 17000.

Q: What is the sum of the divisors of 17000?

The sum is 1 + 2 + 4 + 5 + 8 + 10 + 17 + 20 + 25 + 34 + 40 + 50 + 68 + 85 + 100 + 125 + 136 + 170 + 200 + 250 + 340 + 425 + 500 + 680 + 850 + 1000 + 1700 + 2125 + 3400 + 4250 + 8500 + 17000 = 42120.

Quick Answer

17000 has 32 divisors (factors): 1, 2, 4, 5, 8, 10, 17, 20, 25, 34, 40, 50, 68, 85, 100, 125, 136, 170, 200, 250, 340, 425, 500, 680, 850, 1000, 1700, 2125, 3400, 4250, 8500, 17000.

Sum: 42120.

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 17000

The number 17000 has 32 divisors:

1, 2, 4, 5, 8, 10, 17, 20, 25, 34, 40, 50, 68, 85, 100, 125, 136, 170, 200, 250, 340, 425, 500, 680, 850, 1000, 1700, 2125, 3400, 4250, 8500, 17000

Divisor Pairs of 17000

Each pair multiplies to 17000:

Factor 1	×	Factor 2	=	Product
1	×	17000	=	17000
2	×	8500	=	17000
4	×	4250	=	17000
5	×	3400	=	17000
8	×	2125	=	17000
10	×	1700	=	17000
17	×	1000	=	17000
20	×	850	=	17000
25	×	680	=	17000
34	×	500	=	17000
40	×	425	=	17000
50	×	340	=	17000
68	×	250	=	17000
85	×	200	=	17000
100	×	170	=	17000
125	×	136	=	17000

Number of Divisors

The number 17000 has 32 divisors, written as τ(17000) = 32 in number theory.

Sum of Divisors

σ(17000) = 1 + 2 + 4 + 5 + 8 + 10 + 17 + 20 + 25 + 34 + 40 + 50 + 68 + 85 + 100 + 125 + 136 + 170 + 200 + 250 + 340 + 425 + 500 + 680 + 850 + 1000 + 1700 + 2125 + 3400 + 4250 + 8500 + 17000 = 42120

Prime Factorization of 17000

See the full prime factorization calculator →

Properties of 17000

17000 is composite.
17000 is not a perfect square.
Number of divisors: 32.
Sum of divisors: 42120.

Common Divisors with Another Number?

Looking for the divisors that 17000 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 17000

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √17000 ≈ 130.38. If i divides 17000, then both i and 17000/i are divisors.

1 divides 17000 (17000 ÷ 1 = 17000) → pair (1, 17000)
2 divides 17000 (17000 ÷ 2 = 8500) → pair (2, 8500)
4 divides 17000 (17000 ÷ 4 = 4250) → pair (4, 4250)
5 divides 17000 (17000 ÷ 5 = 3400) → pair (5, 3400)
8 divides 17000 (17000 ÷ 8 = 2125) → pair (8, 2125)
10 divides 17000 (17000 ÷ 10 = 1700) → pair (10, 1700)
17 divides 17000 (17000 ÷ 17 = 1000) → pair (17, 1000)
20 divides 17000 (17000 ÷ 20 = 850) → pair (20, 850)
25 divides 17000 (17000 ÷ 25 = 680) → pair (25, 680)
34 divides 17000 (17000 ÷ 34 = 500) → pair (34, 500)
40 divides 17000 (17000 ÷ 40 = 425) → pair (40, 425)
50 divides 17000 (17000 ÷ 50 = 340) → pair (50, 340)
68 divides 17000 (17000 ÷ 68 = 250) → pair (68, 250)
85 divides 17000 (17000 ÷ 85 = 200) → pair (85, 200)
100 divides 17000 (17000 ÷ 100 = 170) → pair (100, 170)
125 divides 17000 (17000 ÷ 125 = 136) → pair (125, 136)
Collect all unique values: {1, 2, 4, 5, 8, 10, 17, 20, 25, 34, 40, 50, 68, 85, 100, 125, 136, 170, 200, 250, 340, 425, 500, 680, 850, 1000, 1700, 2125, 3400, 4250, 8500, 17000} — total 32 divisors.
Sum: 1 + 2 + 4 + 5 + 8 + 10 + 17 + 20 + 25 + 34 + 40 + 50 + 68 + 85 + 100 + 125 + 136 + 170 + 200 + 250 + 340 + 425 + 500 + 680 + 850 + 1000 + 1700 + 2125 + 3400 + 4250 + 8500 + 17000 = 42120.

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 17000

Multiples of a Number — "outward" complement of divisors
17000 Prime Factorization — decompose into prime building blocks
Find GCF of 17000 and another number
Find LCM of 17000 and another number
Is 17000 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