The number 39744
39744 is a composite number with 56 divisors. Its prime factorisation is × × 23. Divisors (56): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 23, 24, 27, 32, 36, 46 … 39744.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 39744: a Harshad number: divisible by its digit sum 27.
- 2
39744 is composite. Its prime factorisation is
- 3
The divisors add up to 121920; without 39744 itself that is 82176, so 39744 is abundant (82176 is more than 39744). Euler's totient φ(39744) = 12672 numbers up to 39744 share no factor with it.
- 4
The digits of 39744 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 93 steps to reach 1.
LaTeX source of the formulas on this page
\[ 39744 = 2^{6} \times 3^{3} \times 23 \]39744 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 56 |
| Sum of divisors | 121920 |
| Euler totient φ(n) | 12672 |
| Square | 1579585536 |
| Cube | 62779047542784 |
| Square root | 199.358973 (= 24√69) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 93 |
| Scientific notation | 3.9744 × |
39744 in other forms
| Form | Value |
|---|---|
| In words | thirty-nine thousand seven hundred and forty-four |
| Binary (base 2) | 1001101101000000 |
| Octal (base 8) | 115500 |
| Hexadecimal (base 16) | 9B40 |
| Base 3 | 2000112000 |
| As time | 39744 seconds = 11 h 2 min 24 s |
Is 39744 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (39744 ÷ 2 = 19872) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (39744 ÷ 3 = 13248) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (39744 ÷ 4 = 9936) | 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 (39744 ÷ 6 = 6624) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (39744 ÷ 8 = 4968) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (39744 ÷ 9 = 4416) | 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 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (39744 ÷ 12 = 3312) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 39744 a prime number?
No. 39744 = × × 23, so it is divisible by 2.
What are the factors of 39744?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 23, 24, 27, 32, 36, 46, 48, 54, 64, 69, 72, 92, 96, 108, 138, 144, 184, 192, 207, 216, 276, 288, 368, 414, 432, 552, 576, 621, 736, 828, 864, 1104, 1242, 1472, 1656, 1728, 2208, 2484, 3312, 4416, 4968, 6624, 9936, 13248, 19872, 39744.
What is 39744 in binary?
1001101101000000 (hexadecimal 9B40, octal 115500).
What is the square root of 39744?
About 199.3590, exactly 24√69.
Is 39744 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 39744?
39744 is a Harshad number: divisible by its digit sum 27.