The number 10064
10064 is a composite number with 20 divisors. Its prime factorisation is × 17 × 37. Divisors (20): 1, 2, 4, 8, 16, 17, 34, 37, 68, 74, 136, 148, 272, 296, 592, 629 … 10064.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
10064 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
10064 is composite. Its prime factorisation is
- 3
The divisors add up to 21204; without 10064 itself that is 11140, so 10064 is abundant (11140 is more than 10064). Euler's totient φ(10064) = 4608 numbers up to 10064 share no factor with it.
- 4
The digits of 10064 add up to 11, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 42 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10064 = 2^{4} \times 17 \times 37 \]10064 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 21204 |
| Euler totient φ(n) | 4608 |
| Square | 101284096 |
| Cube | 1019323142144 |
| Square root | 100.319490 (= 4√629) |
| Digit sum / digital root | 11 / 2 |
| Collatz steps to 1 | 42 |
| Scientific notation | 1.0064 × |
10064 in other forms
| Form | Value |
|---|---|
| In words | ten thousand and sixty-four |
| Binary (base 2) | 10011101010000 |
| Octal (base 8) | 23520 |
| Hexadecimal (base 16) | 2750 |
| Base 3 | 111210202 |
| As time | 10064 seconds = 2 h 47 min 44 s |
Is 10064 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (10064 ÷ 2 = 5032) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (10064 ÷ 4 = 2516) | 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 2) | 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 (10064 ÷ 8 = 1258) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 2) | 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 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 10064 a prime number?
No. 10064 = × 17 × 37, so it is divisible by 2.
What are the factors of 10064?
1, 2, 4, 8, 16, 17, 34, 37, 68, 74, 136, 148, 272, 296, 592, 629, 1258, 2516, 5032, 10064.
What is 10064 in binary?
10011101010000 (hexadecimal 2750, octal 23520).
What is the square root of 10064?
About 100.3195, exactly 4√629.
Is 10064 divisible by 3?
No. Its digits add up to 11, which is not a multiple of 3.
What is special about the number 10064?
It is a composite number with 20 divisors.