The number 5184
5184 is a perfect square (72²). Its prime factorisation is × . Divisors (35): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54 … 5184.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 5184: a perfect square (72²); a Harshad number: divisible by its digit sum 18.
- 2
5184 is composite. Its prime factorisation is
- 3
The divisors add up to 15367; without 5184 itself that is 10183, so 5184 is abundant (10183 is more than 5184). Euler's totient φ(5184) = 1728 numbers up to 5184 share no factor with it.
- 4
The digits of 5184 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 28 steps to reach 1.
LaTeX source of the formulas on this page
\[ 5184 = 2^{6} \times 3^{4} \]5184 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 35 |
| Sum of divisors | 15367 |
| Euler totient φ(n) | 1728 |
| Square | 26873856 |
| Cube | 139314069504 |
| Square root | 72 |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 28 |
| Scientific notation | 5.184 × |
| Perfect power |
5184 in other forms
| Form | Value |
|---|---|
| In words | five thousand one hundred and eighty-four |
| Binary (base 2) | 1010001000000 |
| Octal (base 8) | 12100 |
| Hexadecimal (base 16) | 1440 |
| Base 3 | 21010000 |
| As time | 5184 seconds = 1 h 26 min 24 s |
Is 5184 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (5184 ÷ 2 = 2592) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (5184 ÷ 3 = 1728) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (5184 ÷ 4 = 1296) | 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 (5184 ÷ 6 = 864) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 (5184 ÷ 8 = 648) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (5184 ÷ 9 = 576) | 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 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (5184 ÷ 12 = 432) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 5184 a prime number?
No. 5184 = × , so it is divisible by 2.
What are the factors of 5184?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 81, 96, 108, 144, 162, 192, 216, 288, 324, 432, 576, 648, 864, 1296, 1728, 2592, 5184.
What is 5184 in binary?
1010001000000 (hexadecimal 1440, octal 12100).
What is the square root of 5184?
72, because 72 × 72 = 5184.
Is 5184 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 5184?
5184 is a perfect square (72²); a Harshad number: divisible by its digit sum 18.