The number 34008
34008 is a composite number with 32 divisors. Its prime factorisation is × 3 × 13 × 109. Divisors (32): 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 109, 156 … 34008.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
34008 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
34008 is composite. Its prime factorisation is
- 3
The divisors add up to 92400; without 34008 itself that is 58392, so 34008 is abundant (58392 is more than 34008). Euler's totient φ(34008) = 10368 numbers up to 34008 share no factor with it.
- 4
The digits of 34008 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 85 steps to reach 1.
LaTeX source of the formulas on this page
\[ 34008 = 2^{3} \times 3 \times 13 \times 109 \]34008 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 92400 |
| Euler totient φ(n) | 10368 |
| Square | 1156544064 |
| Cube | 39331750528512 |
| Square root | 184.412581 (= 2√8502) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 85 |
| Scientific notation | 3.4008 × |
34008 in other forms
| Form | Value |
|---|---|
| In words | thirty-four thousand and eight |
| Binary (base 2) | 1000010011011000 |
| Octal (base 8) | 102330 |
| Hexadecimal (base 16) | 84D8 |
| Base 3 | 1201122120 |
| As time | 34008 seconds = 9 h 26 min 48 s |
Is 34008 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (34008 ÷ 2 = 17004) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (34008 ÷ 3 = 11336) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (34008 ÷ 4 = 8502) | 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 (34008 ÷ 6 = 5668) | 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 (34008 ÷ 8 = 4251) | 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 | 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 (34008 ÷ 12 = 2834) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 34008 a prime number?
No. 34008 = × 3 × 13 × 109, so it is divisible by 2.
What are the factors of 34008?
1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 109, 156, 218, 312, 327, 436, 654, 872, 1308, 1417, 2616, 2834, 4251, 5668, 8502, 11336, 17004, 34008.
What is 34008 in binary?
1000010011011000 (hexadecimal 84D8, octal 102330).
What is the square root of 34008?
About 184.4126, exactly 2√8502.
Is 34008 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 34008?
It is a composite number with 32 divisors.