The number 40320
40320 is 8! (8 factorial). Its prime factorisation is × × 5 × 7. Divisors (96): 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20 … 40320.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 40320: 8! (8 factorial); a Harshad number: divisible by its digit sum 9.
- 2
40320 is composite. Its prime factorisation is
- 3
The divisors add up to 159120; without 40320 itself that is 118800, so 40320 is abundant (118800 is more than 40320). Euler's totient φ(40320) = 9216 numbers up to 40320 share no factor with it.
- 4
The digits of 40320 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 44 steps to reach 1.
LaTeX source of the formulas on this page
\[ 40320 = 2^{7} \times 3^{2} \times 5 \times 7 \]40320 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 96 |
| Sum of divisors | 159120 |
| Euler totient φ(n) | 9216 |
| Square | 1625702400 |
| Cube | 65548320768000 |
| Square root | 200.798406 (= 24√70) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 44 |
| Scientific notation | 4.032 × |
40320 in other forms
| Form | Value |
|---|---|
| In words | forty thousand three hundred and twenty |
| Binary (base 2) | 1001110110000000 |
| Octal (base 8) | 116600 |
| Hexadecimal (base 16) | 9D80 |
| Base 3 | 2001022100 |
| As time | 40320 seconds = 11 h 12 min 0 s |
Is 40320 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (40320 ÷ 2 = 20160) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (40320 ÷ 3 = 13440) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (40320 ÷ 4 = 10080) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (40320 ÷ 5 = 8064) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (40320 ÷ 6 = 6720) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (40320 ÷ 7 = 5760) | 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 (40320 ÷ 8 = 5040) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (40320 ÷ 9 = 4480) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (40320 ÷ 10 = 4032) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (40320 ÷ 12 = 3360) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 40320 a prime number?
No. 40320 = × × 5 × 7, so it is divisible by 2.
What are the factors of 40320?
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 32, 35, 36, 40, 42, 45, 48, 56, 60, 63, 64, 70, 72, 80, 84, 90, 96, 105, 112, 120, 126, 128, 140, 144, 160, 168, 180, 192, 210, 224, 240, 252, 280, 288, 315, 320, 336, 360, 384, 420, 448, 480, 504, 560, 576, 630, 640, 672, 720, 840, 896, 960, 1008, 1120, 1152, 1260, 1344, 1440, 1680, 1920, 2016, 2240, 2520, 2688, 2880, 3360, 4032, 4480, 5040, 5760, 6720, 8064, 10080, 13440, 20160, 40320.
What is 40320 in binary?
1001110110000000 (hexadecimal 9D80, octal 116600).
What is the square root of 40320?
About 200.7984, exactly 24√70.
Is 40320 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 40320?
40320 is 8! (8 factorial); a Harshad number: divisible by its digit sum 9.