The number 78000
78000 is a composite number with 80 divisors. Its prime factorisation is × 3 × × 13. Divisors (80): 1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 16, 20, 24, 25, 26 … 78000.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 78000: a Harshad number: divisible by its digit sum 15.
- 2
78000 is composite. Its prime factorisation is
- 3
The divisors add up to 270816; without 78000 itself that is 192816, so 78000 is abundant (192816 is more than 78000). Euler's totient φ(78000) = 19200 numbers up to 78000 share no factor with it.
- 4
The digits of 78000 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 125 steps to reach 1.
LaTeX source of the formulas on this page
\[ 78000 = 2^{4} \times 3 \times 5^{3} \times 13 \]78000 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 80 |
| Sum of divisors | 270816 |
| Euler totient φ(n) | 19200 |
| Square | 6084000000 |
| Cube | 474552000000000 |
| Square root | 279.284801 (= 20√195) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 125 |
| Scientific notation | 7.8 × |
78000 in other forms
| Form | Value |
|---|---|
| In words | seventy-eight thousand |
| Binary (base 2) | 10011000010110000 |
| Octal (base 8) | 230260 |
| Hexadecimal (base 16) | 130B0 |
| Base 3 | 10221222220 |
| As time | 78000 seconds = 21 h 40 min 0 s |
Is 78000 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (78000 ÷ 2 = 39000) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (78000 ÷ 3 = 26000) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (78000 ÷ 4 = 19500) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (78000 ÷ 5 = 15600) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (78000 ÷ 6 = 13000) | 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 | Yes (78000 ÷ 8 = 9750) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (78000 ÷ 10 = 7800) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (78000 ÷ 12 = 6500) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 78000 a prime number?
No. 78000 = × 3 × × 13, so it is divisible by 2.
What are the factors of 78000?
1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 16, 20, 24, 25, 26, 30, 39, 40, 48, 50, 52, 60, 65, 75, 78, 80, 100, 104, 120, 125, 130, 150, 156, 195, 200, 208, 240, 250, 260, 300, 312, 325, 375, 390, 400, 500, 520, 600, 624, 650, 750, 780, 975, 1000, 1040, 1200, 1300, 1500, 1560, 1625, 1950, 2000, 2600, 3000, 3120, 3250, 3900, 4875, 5200, 6000, 6500, 7800, 9750, 13000, 15600, 19500, 26000, 39000, 78000.
What is 78000 in binary?
10011000010110000 (hexadecimal 130B0, octal 230260).
What is the square root of 78000?
About 279.2848, exactly 20√195.
Is 78000 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 78000?
78000 is a Harshad number: divisible by its digit sum 15.