The number 39312
39312 is a taxicab number: it is the sum of two cubes in 2 ways (2³ + 34³ and 15³ + 33³). Its prime factorisation is × × 7 × 13. Divisors (80): 1, 2, 3, 4, 6, 7, 8, 9, 12, 13, 14, 16, 18, 21, 24, 26 … 39312.
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How to work it out
- 1
What is special about 39312: a taxicab number: it is the sum of two cubes in 2 ways (2³ + 34³ and 15³ + 33³); a Harshad number: divisible by its digit sum 18.
- 2
39312 is composite. Its prime factorisation is
- 3
The divisors add up to 138880; without 39312 itself that is 99568, so 39312 is abundant (99568 is more than 39312). Euler's totient φ(39312) = 10368 numbers up to 39312 share no factor with it.
- 4
The digits of 39312 add up to 18, 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
\[ 39312 = 2^{4} \times 3^{3} \times 7 \times 13 \]39312 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 80 |
| Sum of divisors | 138880 |
| Euler totient φ(n) | 10368 |
| Square | 1545433344 |
| Cube | 60754075619328 |
| Square root | 198.272540 (= 12√273) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 137 |
| Scientific notation | 3.9312 × |
39312 in other forms
| Form | Value |
|---|---|
| In words | thirty-nine thousand three hundred and twelve |
| Binary (base 2) | 1001100110010000 |
| Octal (base 8) | 114620 |
| Hexadecimal (base 16) | 9990 |
| Base 3 | 1222221000 |
| As time | 39312 seconds = 10 h 55 min 12 s |
Is 39312 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (39312 ÷ 2 = 19656) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (39312 ÷ 3 = 13104) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (39312 ÷ 4 = 9828) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (39312 ÷ 6 = 6552) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (39312 ÷ 7 = 5616) | 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 (39312 ÷ 8 = 4914) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (39312 ÷ 9 = 4368) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 2) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (39312 ÷ 12 = 3276) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 39312 a prime number?
No. 39312 = × × 7 × 13, so it is divisible by 2.
What are the factors of 39312?
1, 2, 3, 4, 6, 7, 8, 9, 12, 13, 14, 16, 18, 21, 24, 26, 27, 28, 36, 39, 42, 48, 52, 54, 56, 63, 72, 78, 84, 91, 104, 108, 112, 117, 126, 144, 156, 168, 182, 189, 208, 216, 234, 252, 273, 312, 336, 351, 364, 378, 432, 468, 504, 546, 624, 702, 728, 756, 819, 936, 1008, 1092, 1404, 1456, 1512, 1638, 1872, 2184, 2457, 2808, 3024, 3276, 4368, 4914, 5616, 6552, 9828, 13104, 19656, 39312.
What is 39312 in binary?
1001100110010000 (hexadecimal 9990, octal 114620).
What is the square root of 39312?
About 198.2725, exactly 12√273.
Is 39312 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 39312?
39312 is a taxicab number: it is the sum of two cubes in 2 ways (2³ + 34³ and 15³ + 33³); a Harshad number: divisible by its digit sum 18.