The number 67008
67008 is a composite number with 28 divisors. Its prime factorisation is × 3 × 349. Divisors (28): 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192, 349, 698 … 67008.
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How to work it out
- 1
67008 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
67008 is composite. Its prime factorisation is
- 3
The divisors add up to 177800; without 67008 itself that is 110792, so 67008 is abundant (110792 is more than 67008). Euler's totient φ(67008) = 22272 numbers up to 67008 share no factor with it.
- 4
The digits of 67008 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 130 steps to reach 1.
LaTeX source of the formulas on this page
\[ 67008 = 2^{6} \times 3 \times 349 \]67008 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 28 |
| Sum of divisors | 177800 |
| Euler totient φ(n) | 22272 |
| Square | 4490072064 |
| Cube | 300870748864512 |
| Square root | 258.859035 (= 8√1047) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 130 |
| Scientific notation | 6.7008 × |
67008 in other forms
| Form | Value |
|---|---|
| In words | sixty-seven thousand and eight |
| Binary (base 2) | 10000010111000000 |
| Octal (base 8) | 202700 |
| Hexadecimal (base 16) | 105C0 |
| Base 3 | 10101220210 |
| As time | 67008 seconds = 18 h 36 min 48 s |
Is 67008 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (67008 ÷ 2 = 33504) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (67008 ÷ 3 = 22336) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (67008 ÷ 4 = 16752) | 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 (67008 ÷ 6 = 11168) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 (67008 ÷ 8 = 8376) | 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 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (67008 ÷ 12 = 5584) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 67008 a prime number?
No. 67008 = × 3 × 349, so it is divisible by 2.
What are the factors of 67008?
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192, 349, 698, 1047, 1396, 2094, 2792, 4188, 5584, 8376, 11168, 16752, 22336, 33504, 67008.
What is 67008 in binary?
10000010111000000 (hexadecimal 105C0, octal 202700).
What is the square root of 67008?
About 258.8590, exactly 8√1047.
Is 67008 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 67008?
It is a composite number with 28 divisors.