The number 15360
15360 is a composite number with 44 divisors. Its prime factorisation is × 3 × 5. Divisors (44): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40 … 15360.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 15360: a Harshad number: divisible by its digit sum 15.
- 2
15360 is composite. Its prime factorisation is
- 3
The divisors add up to 49128; without 15360 itself that is 33768, so 15360 is abundant (33768 is more than 15360). Euler's totient φ(15360) = 4096 numbers up to 15360 share no factor with it.
- 4
The digits of 15360 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 27 steps to reach 1.
LaTeX source of the formulas on this page
\[ 15360 = 2^{10} \times 3 \times 5 \]15360 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 44 |
| Sum of divisors | 49128 |
| Euler totient φ(n) | 4096 |
| Square | 235929600 |
| Cube | 3623878656000 |
| Square root | 123.935467 (= 32√15) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 27 |
| Scientific notation | 1.536 × |
15360 in other forms
| Form | Value |
|---|---|
| In words | fifteen thousand three hundred and sixty |
| Binary (base 2) | 11110000000000 |
| Octal (base 8) | 36000 |
| Hexadecimal (base 16) | 3C00 |
| Base 3 | 210001220 |
| As time | 15360 seconds = 4 h 16 min 0 s |
Is 15360 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (15360 ÷ 2 = 7680) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (15360 ÷ 3 = 5120) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (15360 ÷ 4 = 3840) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (15360 ÷ 5 = 3072) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (15360 ÷ 6 = 2560) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 (15360 ÷ 8 = 1920) | 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 (15360 ÷ 10 = 1536) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (15360 ÷ 12 = 1280) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 15360 a prime number?
No. 15360 = × 3 × 5, so it is divisible by 2.
What are the factors of 15360?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 128, 160, 192, 240, 256, 320, 384, 480, 512, 640, 768, 960, 1024, 1280, 1536, 1920, 2560, 3072, 3840, 5120, 7680, 15360.
What is 15360 in binary?
11110000000000 (hexadecimal 3C00, octal 36000).
What is the square root of 15360?
About 123.9355, exactly 32√15.
Is 15360 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 15360?
15360 is a Harshad number: divisible by its digit sum 15.