The number 23184
23184 is a composite number with 60 divisors. Its prime factorisation is × × 7 × 23. Divisors (60): 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 23, 24, 28 … 23184.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 23184: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
23184 is composite. Its prime factorisation is
- 3
The divisors add up to 77376; without 23184 itself that is 54192, so 23184 is abundant (54192 is more than 23184). Euler's totient φ(23184) = 6336 numbers up to 23184 share no factor with it.
- 4
The digits of 23184 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 144 steps to reach 1.
LaTeX source of the formulas on this page
\[ 23184 = 2^{4} \times 3^{2} \times 7 \times 23 \]23184 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 60 |
| Sum of divisors | 77376 |
| Euler totient φ(n) | 6336 |
| Square | 537497856 |
| Cube | 12461350293504 |
| Square root | 152.262930 (= 12√161) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 144 |
| Scientific notation | 2.3184 × |
23184 in other forms
| Form | Value |
|---|---|
| In words | twenty-three thousand one hundred and eighty-four |
| Binary (base 2) | 101101010010000 |
| Octal (base 8) | 55220 |
| Hexadecimal (base 16) | 5A90 |
| Base 3 | 1011210200 |
| As time | 23184 seconds = 6 h 26 min 24 s |
Is 23184 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (23184 ÷ 2 = 11592) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (23184 ÷ 3 = 7728) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (23184 ÷ 4 = 5796) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (23184 ÷ 6 = 3864) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (23184 ÷ 7 = 3312) | 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 (23184 ÷ 8 = 2898) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (23184 ÷ 9 = 2576) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (23184 ÷ 12 = 1932) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 23184 a prime number?
No. 23184 = × × 7 × 23, so it is divisible by 2.
What are the factors of 23184?
1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 23, 24, 28, 36, 42, 46, 48, 56, 63, 69, 72, 84, 92, 112, 126, 138, 144, 161, 168, 184, 207, 252, 276, 322, 336, 368, 414, 483, 504, 552, 644, 828, 966, 1008, 1104, 1288, 1449, 1656, 1932, 2576, 2898, 3312, 3864, 5796, 7728, 11592, 23184.
What is 23184 in binary?
101101010010000 (hexadecimal 5A90, octal 55220).
What is the square root of 23184?
About 152.2629, exactly 12√161.
Is 23184 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 23184?
23184 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.