The number 84024
84024 is a composite number with 32 divisors. Its prime factorisation is × × 389. Divisors (32): 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216 … 84024.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 84024: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
84024 is composite. Its prime factorisation is
- 3
The divisors add up to 234000; without 84024 itself that is 149976, so 84024 is abundant (149976 is more than 84024). Euler's totient φ(84024) = 27936 numbers up to 84024 share no factor with it.
- 4
The digits of 84024 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 133 steps to reach 1.
LaTeX source of the formulas on this page
\[ 84024 = 2^{3} \times 3^{3} \times 389 \]84024 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 234000 |
| Euler totient φ(n) | 27936 |
| Square | 7060032576 |
| Cube | 593212177165824 |
| Square root | 289.868936 (= 6√2334) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 133 |
| Scientific notation | 8.4024 × |
84024 in other forms
| Form | Value |
|---|---|
| In words | eighty-four thousand and twenty-four |
| Binary (base 2) | 10100100000111000 |
| Octal (base 8) | 244070 |
| Hexadecimal (base 16) | 14838 |
| Base 3 | 11021021000 |
| As time | 84024 seconds = 23 h 20 min 24 s |
Is 84024 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (84024 ÷ 2 = 42012) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (84024 ÷ 3 = 28008) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (84024 ÷ 4 = 21006) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (84024 ÷ 6 = 14004) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 (84024 ÷ 8 = 10503) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (84024 ÷ 9 = 9336) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (84024 ÷ 12 = 7002) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 84024 a prime number?
No. 84024 = × × 389, so it is divisible by 2.
What are the factors of 84024?
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216, 389, 778, 1167, 1556, 2334, 3112, 3501, 4668, 7002, 9336, 10503, 14004, 21006, 28008, 42012, 84024.
What is 84024 in binary?
10100100000111000 (hexadecimal 14838, octal 244070).
What is the square root of 84024?
About 289.8689, exactly 6√2334.
Is 84024 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 84024?
84024 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.