The number 73920
73920 is a triangular number: 1 + 2 + … + 384 = 73920. Its prime factorisation is × 3 × 5 × 7 × 11. Divisors (112): 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 14, 15, 16, 20, 21 … 73920.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 73920: a triangular number: 1 + 2 + … + 384 = 73920; a Harshad number: divisible by its digit sum 21.
- 2
73920 is composite. Its prime factorisation is
- 3
The divisors add up to 292608; without 73920 itself that is 218688, so 73920 is abundant (218688 is more than 73920). Euler's totient φ(73920) = 15360 numbers up to 73920 share no factor with it.
- 4
The digits of 73920 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 37 steps to reach 1.
LaTeX source of the formulas on this page
\[ 73920 = 2^{6} \times 3 \times 5 \times 7 \times 11 \]73920 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 112 |
| Sum of divisors | 292608 |
| Euler totient φ(n) | 15360 |
| Square | 5464166400 |
| Cube | 403911180288000 |
| Square root | 271.882327 (= 8√1155) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 37 |
| Scientific notation | 7.392 × |
73920 in other forms
| Form | Value |
|---|---|
| In words | seventy-three thousand nine hundred and twenty |
| Binary (base 2) | 10010000011000000 |
| Octal (base 8) | 220300 |
| Hexadecimal (base 16) | 120C0 |
| Base 3 | 10202101210 |
| As time | 73920 seconds = 20 h 32 min 0 s |
Is 73920 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (73920 ÷ 2 = 36960) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (73920 ÷ 3 = 24640) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (73920 ÷ 4 = 18480) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (73920 ÷ 5 = 14784) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (73920 ÷ 6 = 12320) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (73920 ÷ 7 = 10560) | 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 (73920 ÷ 8 = 9240) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (73920 ÷ 10 = 7392) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (73920 ÷ 11 = 6720) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (73920 ÷ 12 = 6160) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 73920 a prime number?
No. 73920 = × 3 × 5 × 7 × 11, so it is divisible by 2.
What are the factors of 73920?
1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 14, 15, 16, 20, 21, 22, 24, 28, 30, 32, 33, 35, 40, 42, 44, 48, 55, 56, 60, 64, 66, 70, 77, 80, 84, 88, 96, 105, 110, 112, 120, 132, 140, 154, 160, 165, 168, 176, 192, 210, 220, 224, 231, 240, 264, 280, 308, 320, 330, 336, 352, 385, 420, 440, 448, 462, 480, 528, 560, 616, 660, 672, 704, 770, 840, 880, 924, 960, 1056, 1120, 1155, 1232, 1320, 1344, 1540, 1680, 1760, 1848, 2112, 2240, 2310, 2464, 2640, 3080, 3360, 3520, 3696, 4620, 4928, 5280, 6160, 6720, 7392, 9240, 10560, 12320, 14784, 18480, 24640, 36960, 73920.
What is 73920 in binary?
10010000011000000 (hexadecimal 120C0, octal 220300).
What is the square root of 73920?
About 271.8823, exactly 8√1155.
Is 73920 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 73920?
73920 is a triangular number: 1 + 2 + … + 384 = 73920; a Harshad number: divisible by its digit sum 21.