Divisors of 34800: 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 34800

The number 34800 has 60 divisors:

1,  2,  3,  4,  5,  6,  8,  10,  12,  15,  16,  20,  24,  25,  29,  30,  40,  48,  50,  58,  60,  75,  80,  87,  100,  116,  120,  145,  150,  174,  200,  232,  240,  290,  300,  348,  400,  435,  464,  580,  600,  696,  725,  870,  1160,  1200,  1392,  1450,  1740,  2175,  2320,  2900,  3480,  4350,  5800,  6960,  8700,  11600,  17400,  34800

Divisor Pairs of 34800

Each pair multiplies to 34800:

Number of Divisors

The number 34800 has 60 divisors, written as τ(34800) = 60 in number theory.

Sum of Divisors

σ(34800) = 1 + 2 + 3 + 4 + 5 + 6 + 8 + 10 + 12 + 15 + 16 + 20 + 24 + 25 + 29 + 30 + 40 + 48 + 50 + 58 + 60 + 75 + 80 + 87 + 100 + 116 + 120 + 145 + 150 + 174 + 200 + 232 + 240 + 290 + 300 + 348 + 400 + 435 + 464 + 580 + 600 + 696 + 725 + 870 + 1160 + 1200 + 1392 + 1450 + 1740 + 2175 + 2320 + 2900 + 3480 + 4350 + 5800 + 6960 + 8700 + 11600 + 17400 + 34800 = 115320

Prime Factorization of 34800

See the full prime factorization calculator →

Properties of 34800

• 34800 is composite.
• 34800 is not a perfect square.
• Number of divisors: 60.
• Sum of divisors: 115320.

Common Divisors with Another Number?

Looking for the divisors that 34800 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 34800

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √34800 ≈ 186.55. If i divides 34800, then both i and 34800/i are divisors.

1. 1 divides 34800 (34800 ÷ 1 = 34800) → pair (1, 34800)
2. 2 divides 34800 (34800 ÷ 2 = 17400) → pair (2, 17400)
3. 3 divides 34800 (34800 ÷ 3 = 11600) → pair (3, 11600)
4. 4 divides 34800 (34800 ÷ 4 = 8700) → pair (4, 8700)
5. 5 divides 34800 (34800 ÷ 5 = 6960) → pair (5, 6960)
6. 6 divides 34800 (34800 ÷ 6 = 5800) → pair (6, 5800)
7. 8 divides 34800 (34800 ÷ 8 = 4350) → pair (8, 4350)
8. 10 divides 34800 (34800 ÷ 10 = 3480) → pair (10, 3480)
9. 12 divides 34800 (34800 ÷ 12 = 2900) → pair (12, 2900)
10. 15 divides 34800 (34800 ÷ 15 = 2320) → pair (15, 2320)
11. 16 divides 34800 (34800 ÷ 16 = 2175) → pair (16, 2175)
12. 20 divides 34800 (34800 ÷ 20 = 1740) → pair (20, 1740)
13. 24 divides 34800 (34800 ÷ 24 = 1450) → pair (24, 1450)
14. 25 divides 34800 (34800 ÷ 25 = 1392) → pair (25, 1392)
15. 29 divides 34800 (34800 ÷ 29 = 1200) → pair (29, 1200)
16. 30 divides 34800 (34800 ÷ 30 = 1160) → pair (30, 1160)
17. 40 divides 34800 (34800 ÷ 40 = 870) → pair (40, 870)
18. 48 divides 34800 (34800 ÷ 48 = 725) → pair (48, 725)
19. 50 divides 34800 (34800 ÷ 50 = 696) → pair (50, 696)
20. 58 divides 34800 (34800 ÷ 58 = 600) → pair (58, 600)
21. 60 divides 34800 (34800 ÷ 60 = 580) → pair (60, 580)
22. 75 divides 34800 (34800 ÷ 75 = 464) → pair (75, 464)
23. 80 divides 34800 (34800 ÷ 80 = 435) → pair (80, 435)
24. 87 divides 34800 (34800 ÷ 87 = 400) → pair (87, 400)
25. 100 divides 34800 (34800 ÷ 100 = 348) → pair (100, 348)
26. 116 divides 34800 (34800 ÷ 116 = 300) → pair (116, 300)
27. 120 divides 34800 (34800 ÷ 120 = 290) → pair (120, 290)
28. 145 divides 34800 (34800 ÷ 145 = 240) → pair (145, 240)
29. 150 divides 34800 (34800 ÷ 150 = 232) → pair (150, 232)
30. 174 divides 34800 (34800 ÷ 174 = 200) → pair (174, 200)
31. Collect all unique values: {1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 29, 30, 40, 48, 50, 58, 60, 75, 80, 87, 100, 116, 120, 145, 150, 174, 200, 232, 240, 290, 300, 348, 400, 435, 464, 580, 600, 696, 725, 870, 1160, 1200, 1392, 1450, 1740, 2175, 2320, 2900, 3480, 4350, 5800, 6960, 8700, 11600, 17400, 34800} — total 60 divisors.
32. Sum: 1 + 2 + 3 + 4 + 5 + 6 + 8 + 10 + 12 + 15 + 16 + 20 + 24 + 25 + 29 + 30 + 40 + 48 + 50 + 58 + 60 + 75 + 80 + 87 + 100 + 116 + 120 + 145 + 150 + 174 + 200 + 232 + 240 + 290 + 300 + 348 + 400 + 435 + 464 + 580 + 600 + 696 + 725 + 870 + 1160 + 1200 + 1392 + 1450 + 1740 + 2175 + 2320 + 2900 + 3480 + 4350 + 5800 + 6960 + 8700 + 11600 + 17400 + 34800 = 115320.

Nearby Examples

Related Operations for 34800

• Multiples of a Number — "outward" complement of divisors
• 34800 Prime Factorization — decompose into prime building blocks
• Find GCF of 34800 and another number
• Find LCM of 34800 and another number
• Is 34800 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: