The number 8160
8160 is a composite number with 48 divisors. Its prime factorisation is × 3 × 5 × 17. Divisors (48): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 17, 20, 24, 30, 32 … 8160.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 8160: a Harshad number: divisible by its digit sum 15.
- 2
8160 is composite. Its prime factorisation is
- 3
The divisors add up to 27216; without 8160 itself that is 19056, so 8160 is abundant (19056 is more than 8160). Euler's totient φ(8160) = 2048 numbers up to 8160 share no factor with it.
- 4
The digits of 8160 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 52 steps to reach 1.
LaTeX source of the formulas on this page
\[ 8160 = 2^{5} \times 3 \times 5 \times 17 \]8160 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 27216 |
| Euler totient φ(n) | 2048 |
| Square | 66585600 |
| Cube | 543338496000 |
| Square root | 90.332718 (= 4√510) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 52 |
| Scientific notation | 8.16 × |
8160 in other forms
| Form | Value |
|---|---|
| In words | eight thousand one hundred and sixty |
| Binary (base 2) | 1111111100000 |
| Octal (base 8) | 17740 |
| Hexadecimal (base 16) | 1FE0 |
| Base 3 | 102012020 |
| As time | 8160 seconds = 2 h 16 min 0 s |
Is 8160 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (8160 ÷ 2 = 4080) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (8160 ÷ 3 = 2720) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (8160 ÷ 4 = 2040) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (8160 ÷ 5 = 1632) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (8160 ÷ 6 = 1360) | 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 (8160 ÷ 8 = 1020) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (8160 ÷ 10 = 816) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (8160 ÷ 12 = 680) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 8160 a prime number?
No. 8160 = × 3 × 5 × 17, so it is divisible by 2.
What are the factors of 8160?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 17, 20, 24, 30, 32, 34, 40, 48, 51, 60, 68, 80, 85, 96, 102, 120, 136, 160, 170, 204, 240, 255, 272, 340, 408, 480, 510, 544, 680, 816, 1020, 1360, 1632, 2040, 2720, 4080, 8160.
What is 8160 in binary?
1111111100000 (hexadecimal 1FE0, octal 17740).
What is the square root of 8160?
About 90.3327, exactly 4√510.
Is 8160 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 8160?
8160 is a Harshad number: divisible by its digit sum 15.