The number 73440
73440 is a composite number with 96 divisors. Its prime factorisation is × × 5 × 17. Divisors (96): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 17, 18, 20, 24 … 73440.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 73440: a Harshad number: divisible by its digit sum 18.
- 2
73440 is composite. Its prime factorisation is
- 3
The divisors add up to 272160; without 73440 itself that is 198720, so 73440 is abundant (198720 is more than 73440). Euler's totient φ(73440) = 18432 numbers up to 73440 share no factor with it.
- 4
The digits of 73440 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 63 steps to reach 1.
LaTeX source of the formulas on this page
\[ 73440 = 2^{5} \times 3^{3} \times 5 \times 17 \]73440 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 96 |
| Sum of divisors | 272160 |
| Euler totient φ(n) | 18432 |
| Square | 5393433600 |
| Cube | 396093763584000 |
| Square root | 270.998155 (= 12√510) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 63 |
| Scientific notation | 7.344 × |
73440 in other forms
| Form | Value |
|---|---|
| In words | seventy-three thousand four hundred and forty |
| Binary (base 2) | 10001111011100000 |
| Octal (base 8) | 217340 |
| Hexadecimal (base 16) | 11EE0 |
| Base 3 | 10201202000 |
| As time | 73440 seconds = 20 h 24 min 0 s |
Is 73440 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (73440 ÷ 2 = 36720) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (73440 ÷ 3 = 24480) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (73440 ÷ 4 = 18360) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (73440 ÷ 5 = 14688) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (73440 ÷ 6 = 12240) | 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 (73440 ÷ 8 = 9180) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (73440 ÷ 9 = 8160) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (73440 ÷ 10 = 7344) | 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 (73440 ÷ 12 = 6120) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 73440 a prime number?
No. 73440 = × × 5 × 17, so it is divisible by 2.
What are the factors of 73440?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 17, 18, 20, 24, 27, 30, 32, 34, 36, 40, 45, 48, 51, 54, 60, 68, 72, 80, 85, 90, 96, 102, 108, 120, 135, 136, 144, 153, 160, 170, 180, 204, 216, 240, 255, 270, 272, 288, 306, 340, 360, 408, 432, 459, 480, 510, 540, 544, 612, 680, 720, 765, 816, 864, 918, 1020, 1080, 1224, 1360, 1440, 1530, 1632, 1836, 2040, 2160, 2295, 2448, 2720, 3060, 3672, 4080, 4320, 4590, 4896, 6120, 7344, 8160, 9180, 12240, 14688, 18360, 24480, 36720, 73440.
What is 73440 in binary?
10001111011100000 (hexadecimal 11EE0, octal 217340).
What is the square root of 73440?
About 270.9982, exactly 12√510.
Is 73440 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 73440?
73440 is a Harshad number: divisible by its digit sum 18.