The number 8400
8400 is a composite number with 60 divisors. Its prime factorisation is × 3 × × 7. Divisors (60): 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24 … 8400.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 8400: a Harshad number: divisible by its digit sum 12.
- 2
8400 is composite. Its prime factorisation is
- 3
The divisors add up to 30752; without 8400 itself that is 22352, so 8400 is abundant (22352 is more than 8400). Euler's totient φ(8400) = 1920 numbers up to 8400 share no factor with it.
- 4
The digits of 8400 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 34 steps to reach 1.
LaTeX source of the formulas on this page
\[ 8400 = 2^{4} \times 3 \times 5^{2} \times 7 \]8400 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 60 |
| Sum of divisors | 30752 |
| Euler totient φ(n) | 1920 |
| Square | 70560000 |
| Cube | 592704000000 |
| Square root | 91.651514 (= 20√21) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 34 |
| Scientific notation | 8.4 × |
8400 in other forms
| Form | Value |
|---|---|
| In words | eight thousand four hundred |
| Binary (base 2) | 10000011010000 |
| Octal (base 8) | 20320 |
| Hexadecimal (base 16) | 20D0 |
| Base 3 | 102112010 |
| As time | 8400 seconds = 2 h 20 min 0 s |
Is 8400 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (8400 ÷ 2 = 4200) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (8400 ÷ 3 = 2800) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (8400 ÷ 4 = 2100) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (8400 ÷ 5 = 1680) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (8400 ÷ 6 = 1400) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (8400 ÷ 7 = 1200) | A number is divisible by 7 if double the last digit and subtract it from the rest: the result is a multiple of 7. |
| 8 | Yes (8400 ÷ 8 = 1050) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (8400 ÷ 10 = 840) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (8400 ÷ 12 = 700) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 8400 a prime number?
No. 8400 = × 3 × × 7, so it is divisible by 2.
What are the factors of 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.
What is 8400 in binary?
10000011010000 (hexadecimal 20D0, octal 20320).
What is the square root of 8400?
About 91.6515, exactly 20√21.
Is 8400 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 8400?
8400 is a Harshad number: divisible by its digit sum 12.