The number 72960
72960 is a composite number with 72 divisors. Its prime factorisation is × 3 × 5 × 19. Divisors (72): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 19, 20, 24, 30, 32 … 72960.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 72960: a Harshad number: divisible by its digit sum 24.
- 2
72960 is composite. Its prime factorisation is
- 3
The divisors add up to 245280; without 72960 itself that is 172320, so 72960 is abundant (172320 is more than 72960). Euler's totient φ(72960) = 18432 numbers up to 72960 share no factor with it.
- 4
The digits of 72960 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 112 steps to reach 1.
LaTeX source of the formulas on this page
\[ 72960 = 2^{8} \times 3 \times 5 \times 19 \]72960 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 72 |
| Sum of divisors | 245280 |
| Euler totient φ(n) | 18432 |
| Square | 5323161600 |
| Cube | 388377870336000 |
| Square root | 270.111088 (= 16√285) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 112 |
| Scientific notation | 7.296 × |
72960 in other forms
| Form | Value |
|---|---|
| In words | seventy-two thousand nine hundred and sixty |
| Binary (base 2) | 10001110100000000 |
| Octal (base 8) | 216400 |
| Hexadecimal (base 16) | 11D00 |
| Base 3 | 10201002020 |
| As time | 72960 seconds = 20 h 16 min 0 s |
Is 72960 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (72960 ÷ 2 = 36480) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (72960 ÷ 3 = 24320) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (72960 ÷ 4 = 18240) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (72960 ÷ 5 = 14592) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (72960 ÷ 6 = 12160) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 (72960 ÷ 8 = 9120) | 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 (72960 ÷ 10 = 7296) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (72960 ÷ 12 = 6080) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 72960 a prime number?
No. 72960 = × 3 × 5 × 19, so it is divisible by 2.
What are the factors of 72960?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 19, 20, 24, 30, 32, 38, 40, 48, 57, 60, 64, 76, 80, 95, 96, 114, 120, 128, 152, 160, 190, 192, 228, 240, 256, 285, 304, 320, 380, 384, 456, 480, 570, 608, 640, 760, 768, 912, 960, 1140, 1216, 1280, 1520, 1824, 1920, 2280, 2432, 3040, 3648, 3840, 4560, 4864, 6080, 7296, 9120, 12160, 14592, 18240, 24320, 36480, 72960.
What is 72960 in binary?
10001110100000000 (hexadecimal 11D00, octal 216400).
What is the square root of 72960?
About 270.1111, exactly 16√285.
Is 72960 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 72960?
72960 is a Harshad number: divisible by its digit sum 24.