The number 23000
23000 is a composite number with 32 divisors. Its prime factorisation is × × 23. Divisors (32): 1, 2, 4, 5, 8, 10, 20, 23, 25, 40, 46, 50, 92, 100, 115, 125 … 23000.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 23000: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 5.
- 2
23000 is composite. Its prime factorisation is
- 3
The divisors add up to 56160; without 23000 itself that is 33160, so 23000 is abundant (33160 is more than 23000). Euler's totient φ(23000) = 8800 numbers up to 23000 share no factor with it.
- 4
The digits of 23000 add up to 5, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 56 steps to reach 1.
LaTeX source of the formulas on this page
\[ 23000 = 2^{3} \times 5^{3} \times 23 \]23000 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 56160 |
| Euler totient φ(n) | 8800 |
| Square | 529000000 |
| Cube | 12167000000000 |
| Square root | 151.657509 (= 10√230) |
| Digit sum / digital root | 5 / 5 |
| Collatz steps to 1 | 56 |
| Scientific notation | 2.3 × |
23000 in other forms
| Form | Value |
|---|---|
| In words | twenty-three thousand |
| Binary (base 2) | 101100111011000 |
| Octal (base 8) | 54730 |
| Hexadecimal (base 16) | 59D8 |
| Base 3 | 1011112212 |
| As time | 23000 seconds = 6 h 23 min 20 s |
Is 23000 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (23000 ÷ 2 = 11500) | 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 (23000 ÷ 4 = 5750) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (23000 ÷ 5 = 4600) | 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 5) | 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 (23000 ÷ 8 = 2875) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 5) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (23000 ÷ 10 = 2300) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | 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 23000 a prime number?
No. 23000 = × × 23, so it is divisible by 2.
What are the factors of 23000?
1, 2, 4, 5, 8, 10, 20, 23, 25, 40, 46, 50, 92, 100, 115, 125, 184, 200, 230, 250, 460, 500, 575, 920, 1000, 1150, 2300, 2875, 4600, 5750, 11500, 23000.
What is 23000 in binary?
101100111011000 (hexadecimal 59D8, octal 54730).
What is the square root of 23000?
About 151.6575, exactly 10√230.
Is 23000 divisible by 3?
No. Its digits add up to 5, which is not a multiple of 3.
What is special about the number 23000?
23000 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 5.