The number 39888
39888 is a composite number with 30 divisors. Its prime factorisation is × × 277. Divisors (30): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 277 … 39888.
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How to work it out
- 1
What is special about 39888: a Harshad number: divisible by its digit sum 36.
- 2
39888 is composite. Its prime factorisation is
- 3
The divisors add up to 112034; without 39888 itself that is 72146, so 39888 is abundant (72146 is more than 39888). Euler's totient φ(39888) = 13248 numbers up to 39888 share no factor with it.
- 4
The digits of 39888 add up to 36, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 137 steps to reach 1.
LaTeX source of the formulas on this page
\[ 39888 = 2^{4} \times 3^{2} \times 277 \]39888 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 30 |
| Sum of divisors | 112034 |
| Euler totient φ(n) | 13248 |
| Square | 1591052544 |
| Cube | 63463903875072 |
| Square root | 199.719804 (= 12√277) |
| Digit sum / digital root | 36 / 9 |
| Collatz steps to 1 | 137 |
| Scientific notation | 3.9888 × |
39888 in other forms
| Form | Value |
|---|---|
| In words | thirty-nine thousand eight hundred and eighty-eight |
| Binary (base 2) | 1001101111010000 |
| Octal (base 8) | 115720 |
| Hexadecimal (base 16) | 9BD0 |
| Base 3 | 2000201100 |
| As time | 39888 seconds = 11 h 4 min 48 s |
Is 39888 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (39888 ÷ 2 = 19944) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (39888 ÷ 3 = 13296) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (39888 ÷ 4 = 9972) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (39888 ÷ 6 = 6648) | 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 (39888 ÷ 8 = 4986) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (39888 ÷ 9 = 4432) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (39888 ÷ 12 = 3324) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 39888 a prime number?
No. 39888 = × × 277, so it is divisible by 2.
What are the factors of 39888?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 277, 554, 831, 1108, 1662, 2216, 2493, 3324, 4432, 4986, 6648, 9972, 13296, 19944, 39888.
What is 39888 in binary?
1001101111010000 (hexadecimal 9BD0, octal 115720).
What is the square root of 39888?
About 199.7198, exactly 12√277.
Is 39888 divisible by 3?
Yes. Its digits add up to 36, a multiple of 3.
What is special about the number 39888?
39888 is a Harshad number: divisible by its digit sum 36.