The number 13008
13008 is a composite number with 20 divisors. Its prime factorisation is × 3 × 271. Divisors (20): 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 271, 542, 813, 1084, 1626, 2168 … 13008.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13008: a Harshad number: divisible by its digit sum 12.
- 2
13008 is composite. Its prime factorisation is
- 3
The divisors add up to 33728; without 13008 itself that is 20720, so 13008 is abundant (20720 is more than 13008). Euler's totient φ(13008) = 4320 numbers up to 13008 share no factor with it.
- 4
The digits of 13008 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 45 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13008 = 2^{4} \times 3 \times 271 \]13008 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 33728 |
| Euler totient φ(n) | 4320 |
| Square | 169208064 |
| Cube | 2201058496512 |
| Square root | 114.052619 (= 4√813) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 45 |
| Scientific notation | 1.3008 × |
13008 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand and eight |
| Binary (base 2) | 11001011010000 |
| Octal (base 8) | 31320 |
| Hexadecimal (base 16) | 32D0 |
| Base 3 | 122211210 |
| As time | 13008 seconds = 3 h 36 min 48 s |
Is 13008 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13008 ÷ 2 = 6504) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (13008 ÷ 3 = 4336) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (13008 ÷ 4 = 3252) | 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 (13008 ÷ 6 = 2168) | 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 (13008 ÷ 8 = 1626) | 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 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (13008 ÷ 12 = 1084) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13008 a prime number?
No. 13008 = × 3 × 271, so it is divisible by 2.
What are the factors of 13008?
1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 271, 542, 813, 1084, 1626, 2168, 3252, 4336, 6504, 13008.
What is 13008 in binary?
11001011010000 (hexadecimal 32D0, octal 31320).
What is the square root of 13008?
About 114.0526, exactly 4√813.
Is 13008 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 13008?
13008 is a Harshad number: divisible by its digit sum 12.