The number 78084
78084 is a composite number with 30 divisors. Its prime factorisation is × × 241. Divisors (30): 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 241, 324 … 78084.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 78084: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 27.
- 2
78084 is composite. Its prime factorisation is
- 3
The divisors add up to 204974; without 78084 itself that is 126890, so 78084 is abundant (126890 is more than 78084). Euler's totient φ(78084) = 25920 numbers up to 78084 share no factor with it.
- 4
The digits of 78084 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 50 steps to reach 1.
LaTeX source of the formulas on this page
\[ 78084 = 2^{2} \times 3^{4} \times 241 \]78084 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 30 |
| Sum of divisors | 204974 |
| Euler totient φ(n) | 25920 |
| Square | 6097111056 |
| Cube | 476086819696704 |
| Square root | 279.435145 (= 18√241) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 50 |
| Scientific notation | 7.8084 × |
78084 in other forms
| Form | Value |
|---|---|
| In words | seventy-eight thousand and eighty-four |
| Binary (base 2) | 10011000100000100 |
| Octal (base 8) | 230404 |
| Hexadecimal (base 16) | 13104 |
| Base 3 | 10222010000 |
| As time | 78084 seconds = 21 h 41 min 24 s |
Is 78084 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (78084 ÷ 2 = 39042) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (78084 ÷ 3 = 26028) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (78084 ÷ 4 = 19521) | 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 (78084 ÷ 6 = 13014) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (78084 ÷ 9 = 8676) | 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 (78084 ÷ 12 = 6507) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 78084 a prime number?
No. 78084 = × × 241, so it is divisible by 2.
What are the factors of 78084?
1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 241, 324, 482, 723, 964, 1446, 2169, 2892, 4338, 6507, 8676, 13014, 19521, 26028, 39042, 78084.
What is 78084 in binary?
10011000100000100 (hexadecimal 13104, octal 230404).
What is the square root of 78084?
About 279.4351, exactly 18√241.
Is 78084 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 78084?
78084 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 27.