Is 34000 a prime number?

No. 34000 is composite — it has more than 2 divisors (it has 40).

Divisors of 34000: All 40 Factors

Q: What are the divisors of 34000?

The divisors (factors) of 34000 are 1, 2, 4, 5, 8, 10, 16, 17, 20, 25, 34, 40, 50, 68, 80, 85, 100, 125, 136, 170, 200, 250, 272, 340, 400, 425, 500, 680, 850, 1000, 1360, 1700, 2000, 2125, 3400, 4250, 6800, 8500, 17000, 34000.

Q: What is the sum of the divisors of 34000?

The sum is 1 + 2 + 4 + 5 + 8 + 10 + 16 + 17 + 20 + 25 + 34 + 40 + 50 + 68 + 80 + 85 + 100 + 125 + 136 + 170 + 200 + 250 + 272 + 340 + 400 + 425 + 500 + 680 + 850 + 1000 + 1360 + 1700 + 2000 + 2125 + 3400 + 4250 + 6800 + 8500 + 17000 + 34000 = 87048.

Quick Answer

34000 has 40 divisors (factors): 1, 2, 4, 5, 8, 10, 16, 17, 20, 25, 34, 40, 50, 68, 80, 85, 100, 125, 136, 170, 200, 250, 272, 340, 400, 425, 500, 680, 850, 1000, 1360, 1700, 2000, 2125, 3400, 4250, 6800, 8500, 17000, 34000.

Sum: 87048.

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 34000

The number 34000 has 40 divisors:

1, 2, 4, 5, 8, 10, 16, 17, 20, 25, 34, 40, 50, 68, 80, 85, 100, 125, 136, 170, 200, 250, 272, 340, 400, 425, 500, 680, 850, 1000, 1360, 1700, 2000, 2125, 3400, 4250, 6800, 8500, 17000, 34000

Divisor Pairs of 34000

Each pair multiplies to 34000:

Factor 1	×	Factor 2	=	Product
1	×	34000	=	34000
2	×	17000	=	34000
4	×	8500	=	34000
5	×	6800	=	34000
8	×	4250	=	34000
10	×	3400	=	34000
16	×	2125	=	34000
17	×	2000	=	34000
20	×	1700	=	34000
25	×	1360	=	34000
34	×	1000	=	34000
40	×	850	=	34000
50	×	680	=	34000
68	×	500	=	34000
80	×	425	=	34000
85	×	400	=	34000
100	×	340	=	34000
125	×	272	=	34000
136	×	250	=	34000
170	×	200	=	34000

Number of Divisors

The number 34000 has 40 divisors, written as τ(34000) = 40 in number theory.

Sum of Divisors

σ(34000) = 1 + 2 + 4 + 5 + 8 + 10 + 16 + 17 + 20 + 25 + 34 + 40 + 50 + 68 + 80 + 85 + 100 + 125 + 136 + 170 + 200 + 250 + 272 + 340 + 400 + 425 + 500 + 680 + 850 + 1000 + 1360 + 1700 + 2000 + 2125 + 3400 + 4250 + 6800 + 8500 + 17000 + 34000 = 87048

Prime Factorization of 34000

See the full prime factorization calculator →

Properties of 34000

34000 is composite.
34000 is not a perfect square.
Number of divisors: 40.
Sum of divisors: 87048.

Common Divisors with Another Number?

Looking for the divisors that 34000 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 34000

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √34000 ≈ 184.39. If i divides 34000, then both i and 34000/i are divisors.

1 divides 34000 (34000 ÷ 1 = 34000) → pair (1, 34000)
2 divides 34000 (34000 ÷ 2 = 17000) → pair (2, 17000)
4 divides 34000 (34000 ÷ 4 = 8500) → pair (4, 8500)
5 divides 34000 (34000 ÷ 5 = 6800) → pair (5, 6800)
8 divides 34000 (34000 ÷ 8 = 4250) → pair (8, 4250)
10 divides 34000 (34000 ÷ 10 = 3400) → pair (10, 3400)
16 divides 34000 (34000 ÷ 16 = 2125) → pair (16, 2125)
17 divides 34000 (34000 ÷ 17 = 2000) → pair (17, 2000)
20 divides 34000 (34000 ÷ 20 = 1700) → pair (20, 1700)
25 divides 34000 (34000 ÷ 25 = 1360) → pair (25, 1360)
34 divides 34000 (34000 ÷ 34 = 1000) → pair (34, 1000)
40 divides 34000 (34000 ÷ 40 = 850) → pair (40, 850)
50 divides 34000 (34000 ÷ 50 = 680) → pair (50, 680)
68 divides 34000 (34000 ÷ 68 = 500) → pair (68, 500)
80 divides 34000 (34000 ÷ 80 = 425) → pair (80, 425)
85 divides 34000 (34000 ÷ 85 = 400) → pair (85, 400)
100 divides 34000 (34000 ÷ 100 = 340) → pair (100, 340)
125 divides 34000 (34000 ÷ 125 = 272) → pair (125, 272)
136 divides 34000 (34000 ÷ 136 = 250) → pair (136, 250)
170 divides 34000 (34000 ÷ 170 = 200) → pair (170, 200)
Collect all unique values: {1, 2, 4, 5, 8, 10, 16, 17, 20, 25, 34, 40, 50, 68, 80, 85, 100, 125, 136, 170, 200, 250, 272, 340, 400, 425, 500, 680, 850, 1000, 1360, 1700, 2000, 2125, 3400, 4250, 6800, 8500, 17000, 34000} — total 40 divisors.
Sum: 1 + 2 + 4 + 5 + 8 + 10 + 16 + 17 + 20 + 25 + 34 + 40 + 50 + 68 + 80 + 85 + 100 + 125 + 136 + 170 + 200 + 250 + 272 + 340 + 400 + 425 + 500 + 680 + 850 + 1000 + 1360 + 1700 + 2000 + 2125 + 3400 + 4250 + 6800 + 8500 + 17000 + 34000 = 87048.

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 34000

Multiples of a Number — "outward" complement of divisors
34000 Prime Factorization — decompose into prime building blocks
Find GCF of 34000 and another number
Find LCM of 34000 and another number
Is 34000 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