The number 10624
10624 is a composite number with 16 divisors. Its prime factorisation is × 83. Divisors (16): 1, 2, 4, 8, 16, 32, 64, 83, 128, 166, 332, 664, 1328, 2656, 5312, 10624.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
10624 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
10624 is composite. Its prime factorisation is
- 3
The divisors add up to 21420; without 10624 itself that is 10796, so 10624 is abundant (10796 is more than 10624). Euler's totient φ(10624) = 5248 numbers up to 10624 share no factor with it.
- 4
The digits of 10624 add up to 13, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 117 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10624 = 2^{7} \times 83 \]10624 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 21420 |
| Euler totient φ(n) | 5248 |
| Square | 112869376 |
| Cube | 1199124250624 |
| Square root | 103.072790 (= 8√166) |
| Digit sum / digital root | 13 / 4 |
| Collatz steps to 1 | 117 |
| Scientific notation | 1.0624 × |
10624 in other forms
| Form | Value |
|---|---|
| In words | ten thousand six hundred and twenty-four |
| Binary (base 2) | 10100110000000 |
| Octal (base 8) | 24600 |
| Hexadecimal (base 16) | 2980 |
| Base 3 | 112120111 |
| As time | 10624 seconds = 2 h 57 min 4 s |
Is 10624 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (10624 ÷ 2 = 5312) | 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 (10624 ÷ 4 = 2656) | 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 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 (10624 ÷ 8 = 1328) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 4) | 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 9) | 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 10624 a prime number?
No. 10624 = × 83, so it is divisible by 2.
What are the factors of 10624?
1, 2, 4, 8, 16, 32, 64, 83, 128, 166, 332, 664, 1328, 2656, 5312, 10624.
What is 10624 in binary?
10100110000000 (hexadecimal 2980, octal 24600).
What is the square root of 10624?
About 103.0728, exactly 8√166.
Is 10624 divisible by 3?
No. Its digits add up to 13, which is not a multiple of 3.
What is special about the number 10624?
It is a composite number with 16 divisors.