The number 12960
12960 is a composite number with 60 divisors. Its prime factorisation is × × 5. Divisors (60): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 27 … 12960.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 12960: a Harshad number: divisible by its digit sum 18.
- 2
12960 is composite. Its prime factorisation is
- 3
The divisors add up to 45738; without 12960 itself that is 32778, so 12960 is abundant (32778 is more than 12960). Euler's totient φ(12960) = 3456 numbers up to 12960 share no factor with it.
- 4
The digits of 12960 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 32 steps to reach 1.
LaTeX source of the formulas on this page
\[ 12960 = 2^{5} \times 3^{4} \times 5 \]12960 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 60 |
| Sum of divisors | 45738 |
| Euler totient φ(n) | 3456 |
| Square | 167961600 |
| Cube | 2176782336000 |
| Square root | 113.841996 (= 36√10) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 32 |
| Scientific notation | 1.296 × |
12960 in other forms
| Form | Value |
|---|---|
| In words | twelve thousand nine hundred and sixty |
| Binary (base 2) | 11001010100000 |
| Octal (base 8) | 31240 |
| Hexadecimal (base 16) | 32A0 |
| Base 3 | 122210000 |
| As time | 12960 seconds = 3 h 36 min 0 s |
Is 12960 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (12960 ÷ 2 = 6480) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (12960 ÷ 3 = 4320) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (12960 ÷ 4 = 3240) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (12960 ÷ 5 = 2592) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (12960 ÷ 6 = 2160) | 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 (12960 ÷ 8 = 1620) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (12960 ÷ 9 = 1440) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (12960 ÷ 10 = 1296) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (12960 ÷ 12 = 1080) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 12960 a prime number?
No. 12960 = × × 5, so it is divisible by 2.
What are the factors of 12960?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 27, 30, 32, 36, 40, 45, 48, 54, 60, 72, 80, 81, 90, 96, 108, 120, 135, 144, 160, 162, 180, 216, 240, 270, 288, 324, 360, 405, 432, 480, 540, 648, 720, 810, 864, 1080, 1296, 1440, 1620, 2160, 2592, 3240, 4320, 6480, 12960.
What is 12960 in binary?
11001010100000 (hexadecimal 32A0, octal 31240).
What is the square root of 12960?
About 113.8420, exactly 36√10.
Is 12960 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 12960?
12960 is a Harshad number: divisible by its digit sum 18.