The number 81648
81648 is a composite number with 70 divisors. Its prime factorisation is × × 7. Divisors (70): 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 27, 28 … 81648.
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How to work it out
- 1
What is special about 81648: a Harshad number: divisible by its digit sum 27.
- 2
81648 is composite. Its prime factorisation is
- 3
The divisors add up to 271064; without 81648 itself that is 189416, so 81648 is abundant (189416 is more than 81648). Euler's totient φ(81648) = 23328 numbers up to 81648 share no factor with it.
- 4
The digits of 81648 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 89 steps to reach 1.
LaTeX source of the formulas on this page
\[ 81648 = 2^{4} \times 3^{6} \times 7 \]81648 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 70 |
| Sum of divisors | 271064 |
| Euler totient φ(n) | 23328 |
| Square | 6666395904 |
| Cube | 544297892769792 |
| Square root | 285.741142 (= 108√7) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 89 |
| Scientific notation | 8.1648 × |
81648 in other forms
| Form | Value |
|---|---|
| In words | eighty-one thousand six hundred and forty-eight |
| Binary (base 2) | 10011111011110000 |
| Octal (base 8) | 237360 |
| Hexadecimal (base 16) | 13EF0 |
| Base 3 | 11011000000 |
| As time | 81648 seconds = 22 h 40 min 48 s |
Is 81648 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (81648 ÷ 2 = 40824) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (81648 ÷ 3 = 27216) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (81648 ÷ 4 = 20412) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (81648 ÷ 6 = 13608) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (81648 ÷ 7 = 11664) | 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 (81648 ÷ 8 = 10206) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (81648 ÷ 9 = 9072) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (81648 ÷ 12 = 6804) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 81648 a prime number?
No. 81648 = × × 7, so it is divisible by 2.
What are the factors of 81648?
1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 27, 28, 36, 42, 48, 54, 56, 63, 72, 81, 84, 108, 112, 126, 144, 162, 168, 189, 216, 243, 252, 324, 336, 378, 432, 486, 504, 567, 648, 729, 756, 972, 1008, 1134, 1296, 1458, 1512, 1701, 1944, 2268, 2916, 3024, 3402, 3888, 4536, 5103, 5832, 6804, 9072, 10206, 11664, 13608, 20412, 27216, 40824, 81648.
What is 81648 in binary?
10011111011110000 (hexadecimal 13EF0, octal 237360).
What is the square root of 81648?
About 285.7411, exactly 108√7.
Is 81648 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 81648?
81648 is a Harshad number: divisible by its digit sum 27.