The number 67968
67968 is a composite number with 48 divisors. Its prime factorisation is × × 59. Divisors (48): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 59, 64 … 67968.
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How to work it out
- 1
What is special about 67968: a Harshad number: divisible by its digit sum 36.
- 2
67968 is composite. Its prime factorisation is
- 3
The divisors add up to 198900; without 67968 itself that is 130932, so 67968 is abundant (130932 is more than 67968). Euler's totient φ(67968) = 22272 numbers up to 67968 share no factor with it.
- 4
The digits of 67968 add up to 36, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 130 steps to reach 1.
LaTeX source of the formulas on this page
\[ 67968 = 2^{7} \times 3^{2} \times 59 \]67968 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 198900 |
| Euler totient φ(n) | 22272 |
| Square | 4619649024 |
| Cube | 313988304863232 |
| Square root | 260.706732 (= 24√118) |
| Digit sum / digital root | 36 / 9 |
| Collatz steps to 1 | 130 |
| Scientific notation | 6.7968 × |
67968 in other forms
| Form | Value |
|---|---|
| In words | sixty-seven thousand nine hundred and sixty-eight |
| Binary (base 2) | 10000100110000000 |
| Octal (base 8) | 204600 |
| Hexadecimal (base 16) | 10980 |
| Base 3 | 10110020100 |
| As time | 67968 seconds = 18 h 52 min 48 s |
Is 67968 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (67968 ÷ 2 = 33984) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (67968 ÷ 3 = 22656) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (67968 ÷ 4 = 16992) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (67968 ÷ 6 = 11328) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (67968 ÷ 8 = 8496) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (67968 ÷ 9 = 7552) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | 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 (67968 ÷ 12 = 5664) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 67968 a prime number?
No. 67968 = × × 59, so it is divisible by 2.
What are the factors of 67968?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 59, 64, 72, 96, 118, 128, 144, 177, 192, 236, 288, 354, 384, 472, 531, 576, 708, 944, 1062, 1152, 1416, 1888, 2124, 2832, 3776, 4248, 5664, 7552, 8496, 11328, 16992, 22656, 33984, 67968.
What is 67968 in binary?
10000100110000000 (hexadecimal 10980, octal 204600).
What is the square root of 67968?
About 260.7067, exactly 24√118.
Is 67968 divisible by 3?
Yes. Its digits add up to 36, a multiple of 3.
What is special about the number 67968?
67968 is a Harshad number: divisible by its digit sum 36.