Divisors of 8400: 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 8400

The number 8400 has 60 divisors:

1,  2,  3,  4,  5,  6,  7,  8,  10,  12,  14,  15,  16,  20,  21,  24,  25,  28,  30,  35,  40,  42,  48,  50,  56,  60,  70,  75,  80,  84,  100,  105,  112,  120,  140,  150,  168,  175,  200,  210,  240,  280,  300,  336,  350,  400,  420,  525,  560,  600,  700,  840,  1050,  1200,  1400,  1680,  2100,  2800,  4200,  8400

Divisor Pairs of 8400

Each pair multiplies to 8400:

Number of Divisors

The number 8400 has 60 divisors, written as τ(8400) = 60 in number theory.

Sum of Divisors

σ(8400) = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 10 + 12 + 14 + 15 + 16 + 20 + 21 + 24 + 25 + 28 + 30 + 35 + 40 + 42 + 48 + 50 + 56 + 60 + 70 + 75 + 80 + 84 + 100 + 105 + 112 + 120 + 140 + 150 + 168 + 175 + 200 + 210 + 240 + 280 + 300 + 336 + 350 + 400 + 420 + 525 + 560 + 600 + 700 + 840 + 1050 + 1200 + 1400 + 1680 + 2100 + 2800 + 4200 + 8400 = 30752

Prime Factorization of 8400

See the full prime factorization calculator →

Properties of 8400

• 8400 is composite.
• 8400 is not a perfect square.
• Number of divisors: 60.
• Sum of divisors: 30752.

Common Divisors with Another Number?

Looking for the divisors that 8400 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 8400

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √8400 ≈ 91.65. If i divides 8400, then both i and 8400/i are divisors.

1. 1 divides 8400 (8400 ÷ 1 = 8400) → pair (1, 8400)
2. 2 divides 8400 (8400 ÷ 2 = 4200) → pair (2, 4200)
3. 3 divides 8400 (8400 ÷ 3 = 2800) → pair (3, 2800)
4. 4 divides 8400 (8400 ÷ 4 = 2100) → pair (4, 2100)
5. 5 divides 8400 (8400 ÷ 5 = 1680) → pair (5, 1680)
6. 6 divides 8400 (8400 ÷ 6 = 1400) → pair (6, 1400)
7. 7 divides 8400 (8400 ÷ 7 = 1200) → pair (7, 1200)
8. 8 divides 8400 (8400 ÷ 8 = 1050) → pair (8, 1050)
9. 10 divides 8400 (8400 ÷ 10 = 840) → pair (10, 840)
10. 12 divides 8400 (8400 ÷ 12 = 700) → pair (12, 700)
11. 14 divides 8400 (8400 ÷ 14 = 600) → pair (14, 600)
12. 15 divides 8400 (8400 ÷ 15 = 560) → pair (15, 560)
13. 16 divides 8400 (8400 ÷ 16 = 525) → pair (16, 525)
14. 20 divides 8400 (8400 ÷ 20 = 420) → pair (20, 420)
15. 21 divides 8400 (8400 ÷ 21 = 400) → pair (21, 400)
16. 24 divides 8400 (8400 ÷ 24 = 350) → pair (24, 350)
17. 25 divides 8400 (8400 ÷ 25 = 336) → pair (25, 336)
18. 28 divides 8400 (8400 ÷ 28 = 300) → pair (28, 300)
19. 30 divides 8400 (8400 ÷ 30 = 280) → pair (30, 280)
20. 35 divides 8400 (8400 ÷ 35 = 240) → pair (35, 240)
21. 40 divides 8400 (8400 ÷ 40 = 210) → pair (40, 210)
22. 42 divides 8400 (8400 ÷ 42 = 200) → pair (42, 200)
23. 48 divides 8400 (8400 ÷ 48 = 175) → pair (48, 175)
24. 50 divides 8400 (8400 ÷ 50 = 168) → pair (50, 168)
25. 56 divides 8400 (8400 ÷ 56 = 150) → pair (56, 150)
26. 60 divides 8400 (8400 ÷ 60 = 140) → pair (60, 140)
27. 70 divides 8400 (8400 ÷ 70 = 120) → pair (70, 120)
28. 75 divides 8400 (8400 ÷ 75 = 112) → pair (75, 112)
29. 80 divides 8400 (8400 ÷ 80 = 105) → pair (80, 105)
30. 84 divides 8400 (8400 ÷ 84 = 100) → pair (84, 100)
31. Collect all unique values: {1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 25, 28, 30, 35, 40, 42, 48, 50, 56, 60, 70, 75, 80, 84, 100, 105, 112, 120, 140, 150, 168, 175, 200, 210, 240, 280, 300, 336, 350, 400, 420, 525, 560, 600, 700, 840, 1050, 1200, 1400, 1680, 2100, 2800, 4200, 8400} — total 60 divisors.
32. Sum: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 10 + 12 + 14 + 15 + 16 + 20 + 21 + 24 + 25 + 28 + 30 + 35 + 40 + 42 + 48 + 50 + 56 + 60 + 70 + 75 + 80 + 84 + 100 + 105 + 112 + 120 + 140 + 150 + 168 + 175 + 200 + 210 + 240 + 280 + 300 + 336 + 350 + 400 + 420 + 525 + 560 + 600 + 700 + 840 + 1050 + 1200 + 1400 + 1680 + 2100 + 2800 + 4200 + 8400 = 30752.

Nearby Examples

Related Operations for 8400

• Multiples of 8400 — "outward" complement; M is a multiple of 8400 ⇔ 8400 is a divisor of M
• 8400 Prime Factorization — decompose into prime building blocks
• Find GCF of 8400 and another number
• Find LCM of 8400 and another number
• Is 8400 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: