The number 38624
38624 is a composite number with 24 divisors. Its prime factorisation is × 17 × 71. Divisors (24): 1, 2, 4, 8, 16, 17, 32, 34, 68, 71, 136, 142, 272, 284, 544, 568 … 38624.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 38624: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
38624 is composite. Its prime factorisation is
- 3
The divisors add up to 81648; without 38624 itself that is 43024, so 38624 is abundant (43024 is more than 38624). Euler's totient φ(38624) = 17920 numbers up to 38624 share no factor with it.
- 4
The digits of 38624 add up to 23, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 75 steps to reach 1.
LaTeX source of the formulas on this page
\[ 38624 = 2^{5} \times 17 \times 71 \]38624 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 81648 |
| Euler totient φ(n) | 17920 |
| Square | 1491813376 |
| Cube | 57619799834624 |
| Square root | 196.529896 (= 4√2414) |
| Digit sum / digital root | 23 / 5 |
| Collatz steps to 1 | 75 |
| Scientific notation | 3.8624 × |
38624 in other forms
| Form | Value |
|---|---|
| In words | thirty-eight thousand six hundred and twenty-four |
| Binary (base 2) | 1001011011100000 |
| Octal (base 8) | 113340 |
| Hexadecimal (base 16) | 96E0 |
| Base 3 | 1221222112 |
| As time | 38624 seconds = 10 h 43 min 44 s |
Is 38624 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (38624 ÷ 2 = 19312) | 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 (38624 ÷ 4 = 9656) | 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 (38624 ÷ 8 = 4828) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 5) | 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 3) | 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 38624 a prime number?
No. 38624 = × 17 × 71, so it is divisible by 2.
What are the factors of 38624?
1, 2, 4, 8, 16, 17, 32, 34, 68, 71, 136, 142, 272, 284, 544, 568, 1136, 1207, 2272, 2414, 4828, 9656, 19312, 38624.
What is 38624 in binary?
1001011011100000 (hexadecimal 96E0, octal 113340).
What is the square root of 38624?
About 196.5299, exactly 4√2414.
Is 38624 divisible by 3?
No. Its digits add up to 23, which is not a multiple of 3.
What is special about the number 38624?
38624 is a happy number: repeatedly adding the squares of its digits reaches 1.