The number 13002
13002 is a composite number with 16 divisors. Its prime factorisation is 2 × 3 × 11 × 197. Divisors (16): 1, 2, 3, 6, 11, 22, 33, 66, 197, 394, 591, 1182, 2167, 4334, 6501, 13002.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13002: a Harshad number: divisible by its digit sum 6.
- 2
13002 is composite. Its prime factorisation is
- 3
The divisors add up to 28512; without 13002 itself that is 15510, so 13002 is abundant (15510 is more than 13002). Euler's totient φ(13002) = 3920 numbers up to 13002 share no factor with it.
- 4
The digits of 13002 add up to 6, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 138 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13002 = 2 \times 3 \times 11 \times 197 \]
13002 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 28512 |
| Euler totient φ(n) | 3920 |
| Square | 169052004 |
| Cube | 2198014156008 |
| Square root | 114.026313 |
| Digit sum / digital root | 6 / 6 |
| Collatz steps to 1 | 138 |
| Scientific notation | 1.3002 × |
13002 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand and two |
| Binary (base 2) | 11001011001010 |
| Octal (base 8) | 31312 |
| Hexadecimal (base 16) | 32CA |
| Base 3 | 122211120 |
| As time | 13002 seconds = 3 h 36 min 42 s |
Is 13002 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13002 ÷ 2 = 6501) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (13002 ÷ 3 = 4334) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (13002 ÷ 6 = 2167) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 | No (remainder 2) | 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 2) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (13002 ÷ 11 = 1182) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13002 a prime number?
No. 13002 = 2 × 3 × 11 × 197, so it is divisible by 2.
What are the factors of 13002?
1, 2, 3, 6, 11, 22, 33, 66, 197, 394, 591, 1182, 2167, 4334, 6501, 13002.
What is 13002 in binary?
11001011001010 (hexadecimal 32CA, octal 31312).
What is the square root of 13002?
About 114.0263.
Is 13002 divisible by 3?
Yes. Its digits add up to 6, a multiple of 3.
What is special about the number 13002?
13002 is a Harshad number: divisible by its digit sum 6.