The number 38961
38961 is a composite number with 20 divisors. Its prime factorisation is × 13 × 37. Divisors (20): 1, 3, 9, 13, 27, 37, 39, 81, 111, 117, 333, 351, 481, 999, 1053, 1443 … 38961.
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How to work it out
- 1
What is special about 38961: a Harshad number: divisible by its digit sum 27.
- 2
38961 is composite. Its prime factorisation is
- 3
The divisors add up to 64372; without 38961 itself that is 25411, so 38961 is deficient (25411 is less than 38961). Euler's totient φ(38961) = 23328 numbers up to 38961 share no factor with it.
- 4
The digits of 38961 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 199 steps to reach 1.
LaTeX source of the formulas on this page
\[ 38961 = 3^{4} \times 13 \times 37 \]38961 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 64372 |
| Euler totient φ(n) | 23328 |
| Square | 1517959521 |
| Cube | 59141220897681 |
| Square root | 197.385410 (= 9√481) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 199 |
| Scientific notation | 3.8961 × |
38961 in other forms
| Form | Value |
|---|---|
| In words | thirty-eight thousand nine hundred and sixty-one |
| Binary (base 2) | 1001100000110001 |
| Octal (base 8) | 114061 |
| Hexadecimal (base 16) | 9831 |
| Base 3 | 1222110000 |
| As time | 38961 seconds = 10 h 49 min 21 s |
Is 38961 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (38961 ÷ 3 = 12987) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 1) | 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 | No (remainder 3) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 | No (remainder 1) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (38961 ÷ 9 = 4329) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 1) | 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 | No (remainder 9) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 38961 a prime number?
No. 38961 = × 13 × 37, so it is divisible by 3.
What are the factors of 38961?
1, 3, 9, 13, 27, 37, 39, 81, 111, 117, 333, 351, 481, 999, 1053, 1443, 2997, 4329, 12987, 38961.
What is 38961 in binary?
1001100000110001 (hexadecimal 9831, octal 114061).
What is the square root of 38961?
About 197.3854, exactly 9√481.
Is 38961 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 38961?
38961 is a Harshad number: divisible by its digit sum 27.