The number 13000
13000 is a composite number with 32 divisors. Its prime factorisation is × × 13. Divisors (32): 1, 2, 4, 5, 8, 10, 13, 20, 25, 26, 40, 50, 52, 65, 100, 104 … 13000.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13000: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 4.
- 2
13000 is composite. Its prime factorisation is
- 3
The divisors add up to 32760; without 13000 itself that is 19760, so 13000 is abundant (19760 is more than 13000). Euler's totient φ(13000) = 4800 numbers up to 13000 share no factor with it.
- 4
The digits of 13000 add up to 4, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 138 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13000 = 2^{3} \times 5^{3} \times 13 \]13000 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 32760 |
| Euler totient φ(n) | 4800 |
| Square | 169000000 |
| Cube | 2197000000000 |
| Square root | 114.017543 (= 10√130) |
| Digit sum / digital root | 4 / 4 |
| Collatz steps to 1 | 138 |
| Scientific notation | 1.3 × |
13000 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand |
| Binary (base 2) | 11001011001000 |
| Octal (base 8) | 31310 |
| Hexadecimal (base 16) | 32C8 |
| Base 3 | 122211111 |
| As time | 13000 seconds = 3 h 36 min 40 s |
Is 13000 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13000 ÷ 2 = 6500) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (13000 ÷ 4 = 3250) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (13000 ÷ 5 = 2600) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 (13000 ÷ 8 = 1625) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 4) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (13000 ÷ 10 = 1300) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13000 a prime number?
No. 13000 = × × 13, so it is divisible by 2.
What are the factors of 13000?
1, 2, 4, 5, 8, 10, 13, 20, 25, 26, 40, 50, 52, 65, 100, 104, 125, 130, 200, 250, 260, 325, 500, 520, 650, 1000, 1300, 1625, 2600, 3250, 6500, 13000.
What is 13000 in binary?
11001011001000 (hexadecimal 32C8, octal 31310).
What is the square root of 13000?
About 114.0175, exactly 10√130.
Is 13000 divisible by 3?
No. Its digits add up to 4, which is not a multiple of 3.
What is special about the number 13000?
13000 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 4.