The number 81504
81504 is a composite number with 36 divisors. Its prime factorisation is × × 283. Divisors (36): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96 … 81504.
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How to work it out
- 1
What is special about 81504: a Harshad number: divisible by its digit sum 18.
- 2
81504 is composite. Its prime factorisation is
- 3
The divisors add up to 232596; without 81504 itself that is 151092, so 81504 is abundant (151092 is more than 81504). Euler's totient φ(81504) = 27072 numbers up to 81504 share no factor with it.
- 4
The digits of 81504 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 37 steps to reach 1.
LaTeX source of the formulas on this page
\[ 81504 = 2^{5} \times 3^{2} \times 283 \]81504 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 232596 |
| Euler totient φ(n) | 27072 |
| Square | 6642902016 |
| Cube | 541423085912064 |
| Square root | 285.489054 (= 12√566) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 37 |
| Scientific notation | 8.1504 × |
81504 in other forms
| Form | Value |
|---|---|
| In words | eighty-one thousand five hundred and four |
| Binary (base 2) | 10011111001100000 |
| Octal (base 8) | 237140 |
| Hexadecimal (base 16) | 13E60 |
| Base 3 | 11010210200 |
| As time | 81504 seconds = 22 h 38 min 24 s |
Is 81504 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (81504 ÷ 2 = 40752) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (81504 ÷ 3 = 27168) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (81504 ÷ 4 = 20376) | 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 (81504 ÷ 6 = 13584) | 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 (81504 ÷ 8 = 10188) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (81504 ÷ 9 = 9056) | 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 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (81504 ÷ 12 = 6792) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 81504 a prime number?
No. 81504 = × × 283, so it is divisible by 2.
What are the factors of 81504?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 283, 288, 566, 849, 1132, 1698, 2264, 2547, 3396, 4528, 5094, 6792, 9056, 10188, 13584, 20376, 27168, 40752, 81504.
What is 81504 in binary?
10011111001100000 (hexadecimal 13E60, octal 237140).
What is the square root of 81504?
About 285.4891, exactly 12√566.
Is 81504 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 81504?
81504 is a Harshad number: divisible by its digit sum 18.