The number 67104
67104 is a composite number with 36 divisors. Its prime factorisation is × × 233. Divisors (36): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96 … 67104.
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How to work it out
- 1
What is special about 67104: a Harshad number: divisible by its digit sum 18.
- 2
67104 is composite. Its prime factorisation is
- 3
The divisors add up to 191646; without 67104 itself that is 124542, so 67104 is abundant (124542 is more than 67104). Euler's totient φ(67104) = 22272 numbers up to 67104 share no factor with it.
- 4
The digits of 67104 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 68 steps to reach 1.
LaTeX source of the formulas on this page
\[ 67104 = 2^{5} \times 3^{2} \times 233 \]67104 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 191646 |
| Euler totient φ(n) | 22272 |
| Square | 4502946816 |
| Cube | 302165743140864 |
| Square root | 259.044398 (= 12√466) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 68 |
| Scientific notation | 6.7104 × |
67104 in other forms
| Form | Value |
|---|---|
| In words | sixty-seven thousand one hundred and four |
| Binary (base 2) | 10000011000100000 |
| Octal (base 8) | 203040 |
| Hexadecimal (base 16) | 10620 |
| Base 3 | 10102001100 |
| As time | 67104 seconds = 18 h 38 min 24 s |
Is 67104 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (67104 ÷ 2 = 33552) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (67104 ÷ 3 = 22368) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (67104 ÷ 4 = 16776) | 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 (67104 ÷ 6 = 11184) | 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 (67104 ÷ 8 = 8388) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (67104 ÷ 9 = 7456) | 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 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (67104 ÷ 12 = 5592) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 67104 a prime number?
No. 67104 = × × 233, so it is divisible by 2.
What are the factors of 67104?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 233, 288, 466, 699, 932, 1398, 1864, 2097, 2796, 3728, 4194, 5592, 7456, 8388, 11184, 16776, 22368, 33552, 67104.
What is 67104 in binary?
10000011000100000 (hexadecimal 10620, octal 203040).
What is the square root of 67104?
About 259.0444, exactly 12√466.
Is 67104 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 67104?
67104 is a Harshad number: divisible by its digit sum 18.