The number 78024
78024 is a composite number with 16 divisors. Its prime factorisation is × 3 × 3251. Divisors (16): 1, 2, 3, 4, 6, 8, 12, 24, 3251, 6502, 9753, 13004, 19506, 26008, 39012, 78024.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 78024: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
78024 is composite. Its prime factorisation is
- 3
The divisors add up to 195120; without 78024 itself that is 117096, so 78024 is abundant (117096 is more than 78024). Euler's totient φ(78024) = 26000 numbers up to 78024 share no factor with it.
- 4
The digits of 78024 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 125 steps to reach 1.
LaTeX source of the formulas on this page
\[ 78024 = 2^{3} \times 3 \times 3251 \]78024 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 195120 |
| Euler totient φ(n) | 26000 |
| Square | 6087744576 |
| Cube | 474990182797824 |
| Square root | 279.327764 (= 2√19506) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 125 |
| Scientific notation | 7.8024 × |
78024 in other forms
| Form | Value |
|---|---|
| In words | seventy-eight thousand and twenty-four |
| Binary (base 2) | 10011000011001000 |
| Octal (base 8) | 230310 |
| Hexadecimal (base 16) | 130C8 |
| Base 3 | 10222000210 |
| As time | 78024 seconds = 21 h 40 min 24 s |
Is 78024 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (78024 ÷ 2 = 39012) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (78024 ÷ 3 = 26008) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (78024 ÷ 4 = 19506) | 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 (78024 ÷ 6 = 13004) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 (78024 ÷ 8 = 9753) | 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 | No (remainder 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (78024 ÷ 12 = 6502) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 78024 a prime number?
No. 78024 = × 3 × 3251, so it is divisible by 2.
What are the factors of 78024?
1, 2, 3, 4, 6, 8, 12, 24, 3251, 6502, 9753, 13004, 19506, 26008, 39012, 78024.
What is 78024 in binary?
10011000011001000 (hexadecimal 130C8, octal 230310).
What is the square root of 78024?
About 279.3278, exactly 2√19506.
Is 78024 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 78024?
78024 is a happy number: repeatedly adding the squares of its digits reaches 1.