The number 11000
11000 is a composite number with 32 divisors. Its prime factorisation is × × 11. Divisors (32): 1, 2, 4, 5, 8, 10, 11, 20, 22, 25, 40, 44, 50, 55, 88, 100 … 11000.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 11000: a Harshad number: divisible by its digit sum 2.
- 2
11000 is composite. Its prime factorisation is
- 3
The divisors add up to 28080; without 11000 itself that is 17080, so 11000 is abundant (17080 is more than 11000). Euler's totient φ(11000) = 4000 numbers up to 11000 share no factor with it.
- 4
The digits of 11000 add up to 2, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 42 steps to reach 1.
LaTeX source of the formulas on this page
\[ 11000 = 2^{3} \times 5^{3} \times 11 \]11000 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 28080 |
| Euler totient φ(n) | 4000 |
| Square | 121000000 |
| Cube | 1331000000000 |
| Square root | 104.880885 (= 10√110) |
| Digit sum / digital root | 2 / 2 |
| Collatz steps to 1 | 42 |
| Scientific notation | 1.1 × |
11000 in other forms
| Form | Value |
|---|---|
| In words | eleven thousand |
| Binary (base 2) | 10101011111000 |
| Octal (base 8) | 25370 |
| Hexadecimal (base 16) | 2AF8 |
| Base 3 | 120002102 |
| As time | 11000 seconds = 3 h 3 min 20 s |
Is 11000 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (11000 ÷ 2 = 5500) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (11000 ÷ 4 = 2750) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (11000 ÷ 5 = 2200) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 2) | 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 | Yes (11000 ÷ 8 = 1375) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 2) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (11000 ÷ 10 = 1100) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (11000 ÷ 11 = 1000) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 11000 a prime number?
No. 11000 = × × 11, so it is divisible by 2.
What are the factors of 11000?
1, 2, 4, 5, 8, 10, 11, 20, 22, 25, 40, 44, 50, 55, 88, 100, 110, 125, 200, 220, 250, 275, 440, 500, 550, 1000, 1100, 1375, 2200, 2750, 5500, 11000.
What is 11000 in binary?
10101011111000 (hexadecimal 2AF8, octal 25370).
What is the square root of 11000?
About 104.8809, exactly 10√110.
Is 11000 divisible by 3?
No. Its digits add up to 2, which is not a multiple of 3.
What is special about the number 11000?
11000 is a Harshad number: divisible by its digit sum 2.