The number 39984
39984 is a composite number with 60 divisors. Its prime factorisation is × 3 × × 17. Divisors (60): 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 17, 21, 24, 28, 34, 42 … 39984.
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How to work it out
- 1
39984 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
39984 is composite. Its prime factorisation is
- 3
The divisors add up to 127224; without 39984 itself that is 87240, so 39984 is abundant (87240 is more than 39984). Euler's totient φ(39984) = 10752 numbers up to 39984 share no factor with it.
- 4
The digits of 39984 add up to 33, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 181 steps to reach 1.
LaTeX source of the formulas on this page
\[ 39984 = 2^{4} \times 3 \times 7^{2} \times 17 \]39984 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 60 |
| Sum of divisors | 127224 |
| Euler totient φ(n) | 10752 |
| Square | 1598720256 |
| Cube | 63923230715904 |
| Square root | 199.959996 (= 28√51) |
| Digit sum / digital root | 33 / 6 |
| Collatz steps to 1 | 181 |
| Scientific notation | 3.9984 × |
39984 in other forms
| Form | Value |
|---|---|
| In words | thirty-nine thousand nine hundred and eighty-four |
| Binary (base 2) | 1001110000110000 |
| Octal (base 8) | 116060 |
| Hexadecimal (base 16) | 9C30 |
| Base 3 | 2000211220 |
| As time | 39984 seconds = 11 h 6 min 24 s |
Is 39984 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (39984 ÷ 2 = 19992) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (39984 ÷ 3 = 13328) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (39984 ÷ 4 = 9996) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (39984 ÷ 6 = 6664) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (39984 ÷ 7 = 5712) | 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 (39984 ÷ 8 = 4998) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (39984 ÷ 12 = 3332) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 39984 a prime number?
No. 39984 = × 3 × × 17, so it is divisible by 2.
What are the factors of 39984?
1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 17, 21, 24, 28, 34, 42, 48, 49, 51, 56, 68, 84, 98, 102, 112, 119, 136, 147, 168, 196, 204, 238, 272, 294, 336, 357, 392, 408, 476, 588, 714, 784, 816, 833, 952, 1176, 1428, 1666, 1904, 2352, 2499, 2856, 3332, 4998, 5712, 6664, 9996, 13328, 19992, 39984.
What is 39984 in binary?
1001110000110000 (hexadecimal 9C30, octal 116060).
What is the square root of 39984?
About 199.9600, exactly 28√51.
Is 39984 divisible by 3?
Yes. Its digits add up to 33, a multiple of 3.
What is special about the number 39984?
It is a composite number with 60 divisors.