The number 38880
38880 is a composite number with 72 divisors. Its prime factorisation is × × 5. Divisors (72): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 27 … 38880.
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How to work it out
- 1
What is special about 38880: a Harshad number: divisible by its digit sum 27.
- 2
38880 is composite. Its prime factorisation is
- 3
The divisors add up to 137592; without 38880 itself that is 98712, so 38880 is abundant (98712 is more than 38880). Euler's totient φ(38880) = 10368 numbers up to 38880 share no factor with it.
- 4
The digits of 38880 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 168 steps to reach 1.
LaTeX source of the formulas on this page
\[ 38880 = 2^{5} \times 3^{5} \times 5 \]38880 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 72 |
| Sum of divisors | 137592 |
| Euler totient φ(n) | 10368 |
| Square | 1511654400 |
| Cube | 58773123072000 |
| Square root | 197.180121 (= 36√30) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 168 |
| Scientific notation | 3.888 × |
38880 in other forms
| Form | Value |
|---|---|
| In words | thirty-eight thousand eight hundred and eighty |
| Binary (base 2) | 1001011111100000 |
| Octal (base 8) | 113740 |
| Hexadecimal (base 16) | 97E0 |
| Base 3 | 1222100000 |
| As time | 38880 seconds = 10 h 48 min 0 s |
Is 38880 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (38880 ÷ 2 = 19440) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (38880 ÷ 3 = 12960) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (38880 ÷ 4 = 9720) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (38880 ÷ 5 = 7776) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (38880 ÷ 6 = 6480) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 (38880 ÷ 8 = 4860) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (38880 ÷ 9 = 4320) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (38880 ÷ 10 = 3888) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (38880 ÷ 12 = 3240) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 38880 a prime number?
No. 38880 = × × 5, so it is divisible by 2.
What are the factors of 38880?
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, 243, 270, 288, 324, 360, 405, 432, 480, 486, 540, 648, 720, 810, 864, 972, 1080, 1215, 1296, 1440, 1620, 1944, 2160, 2430, 2592, 3240, 3888, 4320, 4860, 6480, 7776, 9720, 12960, 19440, 38880.
What is 38880 in binary?
1001011111100000 (hexadecimal 97E0, octal 113740).
What is the square root of 38880?
About 197.1801, exactly 36√30.
Is 38880 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 38880?
38880 is a Harshad number: divisible by its digit sum 27.