The number 38976
38976 is a composite number with 56 divisors. Its prime factorisation is × 3 × 7 × 29. Divisors (56): 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 29, 32, 42 … 38976.
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How to work it out
- 1
What is special about 38976: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
38976 is composite. Its prime factorisation is
- 3
The divisors add up to 121920; without 38976 itself that is 82944, so 38976 is abundant (82944 is more than 38976). Euler's totient φ(38976) = 10752 numbers up to 38976 share no factor with it.
- 4
The digits of 38976 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 137 steps to reach 1.
LaTeX source of the formulas on this page
\[ 38976 = 2^{6} \times 3 \times 7 \times 29 \]38976 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 56 |
| Sum of divisors | 121920 |
| Euler totient φ(n) | 10752 |
| Square | 1519128576 |
| Cube | 59209555378176 |
| Square root | 197.423403 (= 8√609) |
| Digit sum / digital root | 33 / 6 |
| Collatz steps to 1 | 137 |
| Scientific notation | 3.8976 × |
38976 in other forms
| Form | Value |
|---|---|
| In words | thirty-eight thousand nine hundred and seventy-six |
| Binary (base 2) | 1001100001000000 |
| Octal (base 8) | 114100 |
| Hexadecimal (base 16) | 9840 |
| Base 3 | 1222110120 |
| As time | 38976 seconds = 10 h 49 min 36 s |
Is 38976 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (38976 ÷ 2 = 19488) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (38976 ÷ 3 = 12992) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (38976 ÷ 4 = 9744) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (38976 ÷ 6 = 6496) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (38976 ÷ 7 = 5568) | 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 (38976 ÷ 8 = 4872) | 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 6) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (38976 ÷ 12 = 3248) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 38976 a prime number?
No. 38976 = × 3 × 7 × 29, so it is divisible by 2.
What are the factors of 38976?
1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 29, 32, 42, 48, 56, 58, 64, 84, 87, 96, 112, 116, 168, 174, 192, 203, 224, 232, 336, 348, 406, 448, 464, 609, 672, 696, 812, 928, 1218, 1344, 1392, 1624, 1856, 2436, 2784, 3248, 4872, 5568, 6496, 9744, 12992, 19488, 38976.
What is 38976 in binary?
1001100001000000 (hexadecimal 9840, octal 114100).
What is the square root of 38976?
About 197.4234, exactly 8√609.
Is 38976 divisible by 3?
Yes. Its digits add up to 33, a multiple of 3.
What is special about the number 38976?
38976 is a happy number: repeatedly adding the squares of its digits reaches 1.