The number 68000
68000 is a composite number with 48 divisors. Its prime factorisation is × × 17. Divisors (48): 1, 2, 4, 5, 8, 10, 16, 17, 20, 25, 32, 34, 40, 50, 68, 80 … 68000.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 68000: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
68000 is composite. Its prime factorisation is
- 3
The divisors add up to 176904; without 68000 itself that is 108904, so 68000 is abundant (108904 is more than 68000). Euler's totient φ(68000) = 25600 numbers up to 68000 share no factor with it.
- 4
The digits of 68000 add up to 14, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 130 steps to reach 1.
LaTeX source of the formulas on this page
\[ 68000 = 2^{5} \times 5^{3} \times 17 \]68000 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 176904 |
| Euler totient φ(n) | 25600 |
| Square | 4624000000 |
| Cube | 314432000000000 |
| Square root | 260.768096 (= 20√170) |
| Digit sum / digital root | 14 / 5 |
| Collatz steps to 1 | 130 |
| Scientific notation | 6.8 × |
68000 in other forms
| Form | Value |
|---|---|
| In words | sixty-eight thousand |
| Binary (base 2) | 10000100110100000 |
| Octal (base 8) | 204640 |
| Hexadecimal (base 16) | 109A0 |
| Base 3 | 10110021112 |
| As time | 68000 seconds = 18 h 53 min 20 s |
Is 68000 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (68000 ÷ 2 = 34000) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (68000 ÷ 4 = 17000) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (68000 ÷ 5 = 13600) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 2) | 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 (68000 ÷ 8 = 8500) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 5) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (68000 ÷ 10 = 6800) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 68000 a prime number?
No. 68000 = × × 17, so it is divisible by 2.
What are the factors of 68000?
1, 2, 4, 5, 8, 10, 16, 17, 20, 25, 32, 34, 40, 50, 68, 80, 85, 100, 125, 136, 160, 170, 200, 250, 272, 340, 400, 425, 500, 544, 680, 800, 850, 1000, 1360, 1700, 2000, 2125, 2720, 3400, 4000, 4250, 6800, 8500, 13600, 17000, 34000, 68000.
What is 68000 in binary?
10000100110100000 (hexadecimal 109A0, octal 204640).
What is the square root of 68000?
About 260.7681, exactly 20√170.
Is 68000 divisible by 3?
No. Its digits add up to 14, which is not a multiple of 3.
What is special about the number 68000?
68000 is a happy number: repeatedly adding the squares of its digits reaches 1.