The number 10384
10384 is a composite number with 20 divisors. Its prime factorisation is × 11 × 59. Divisors (20): 1, 2, 4, 8, 11, 16, 22, 44, 59, 88, 118, 176, 236, 472, 649, 944 … 10384.
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How to work it out
- 1
What is special about 10384: a Harshad number: divisible by its digit sum 16.
- 2
10384 is composite. Its prime factorisation is
- 3
The divisors add up to 22320; without 10384 itself that is 11936, so 10384 is abundant (11936 is more than 10384). Euler's totient φ(10384) = 4640 numbers up to 10384 share no factor with it.
- 4
The digits of 10384 add up to 16, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 148 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10384 = 2^{4} \times 11 \times 59 \]10384 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 22320 |
| Euler totient φ(n) | 4640 |
| Square | 107827456 |
| Cube | 1119680303104 |
| Square root | 101.901914 (= 4√649) |
| Digit sum / digital root | 16 / 7 |
| Collatz steps to 1 | 148 |
| Scientific notation | 1.0384 × |
10384 in other forms
| Form | Value |
|---|---|
| In words | ten thousand three hundred and eighty-four |
| Binary (base 2) | 10100010010000 |
| Octal (base 8) | 24220 |
| Hexadecimal (base 16) | 2890 |
| Base 3 | 112020121 |
| As time | 10384 seconds = 2 h 53 min 4 s |
Is 10384 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (10384 ÷ 2 = 5192) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (10384 ÷ 4 = 2596) | 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 | No (remainder 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 (10384 ÷ 8 = 1298) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | 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 | Yes (10384 ÷ 11 = 944) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 10384 a prime number?
No. 10384 = × 11 × 59, so it is divisible by 2.
What are the factors of 10384?
1, 2, 4, 8, 11, 16, 22, 44, 59, 88, 118, 176, 236, 472, 649, 944, 1298, 2596, 5192, 10384.
What is 10384 in binary?
10100010010000 (hexadecimal 2890, octal 24220).
What is the square root of 10384?
About 101.9019, exactly 4√649.
Is 10384 divisible by 3?
No. Its digits add up to 16, which is not a multiple of 3.
What is special about the number 10384?
10384 is a Harshad number: divisible by its digit sum 16.