The number 84000
84000 is a composite number with 96 divisors. Its prime factorisation is × 3 × × 7. Divisors (96): 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24 … 84000.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 84000: a Harshad number: divisible by its digit sum 12.
- 2
84000 is composite. Its prime factorisation is
- 3
The divisors add up to 314496; without 84000 itself that is 230496, so 84000 is abundant (230496 is more than 84000). Euler's totient φ(84000) = 19200 numbers up to 84000 share no factor with it.
- 4
The digits of 84000 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 32 steps to reach 1.
LaTeX source of the formulas on this page
\[ 84000 = 2^{5} \times 3 \times 5^{3} \times 7 \]84000 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 96 |
| Sum of divisors | 314496 |
| Euler totient φ(n) | 19200 |
| Square | 7056000000 |
| Cube | 592704000000000 |
| Square root | 289.827535 (= 20√210) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 32 |
| Scientific notation | 8.4 × |
84000 in other forms
| Form | Value |
|---|---|
| In words | eighty-four thousand |
| Binary (base 2) | 10100100000100000 |
| Octal (base 8) | 244040 |
| Hexadecimal (base 16) | 14820 |
| Base 3 | 11021020010 |
| As time | 84000 seconds = 23 h 20 min 0 s |
Is 84000 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (84000 ÷ 2 = 42000) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (84000 ÷ 3 = 28000) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (84000 ÷ 4 = 21000) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (84000 ÷ 5 = 16800) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (84000 ÷ 6 = 14000) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (84000 ÷ 7 = 12000) | 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 (84000 ÷ 8 = 10500) | 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 (84000 ÷ 10 = 8400) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (84000 ÷ 12 = 7000) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 84000 a prime number?
No. 84000 = × 3 × × 7, so it is divisible by 2.
What are the factors of 84000?
1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 25, 28, 30, 32, 35, 40, 42, 48, 50, 56, 60, 70, 75, 80, 84, 96, 100, 105, 112, 120, 125, 140, 150, 160, 168, 175, 200, 210, 224, 240, 250, 280, 300, 336, 350, 375, 400, 420, 480, 500, 525, 560, 600, 672, 700, 750, 800, 840, 875, 1000, 1050, 1120, 1200, 1400, 1500, 1680, 1750, 2000, 2100, 2400, 2625, 2800, 3000, 3360, 3500, 4000, 4200, 5250, 5600, 6000, 7000, 8400, 10500, 12000, 14000, 16800, 21000, 28000, 42000, 84000.
What is 84000 in binary?
10100100000100000 (hexadecimal 14820, octal 244040).
What is the square root of 84000?
About 289.8275, exactly 20√210.
Is 84000 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 84000?
84000 is a Harshad number: divisible by its digit sum 12.