The number 37638
37638 is a composite number with 32 divisors. Its prime factorisation is 2 × × 17 × 41. Divisors (32): 1, 2, 3, 6, 9, 17, 18, 27, 34, 41, 51, 54, 82, 102, 123, 153 … 37638.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 37638: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 27.
- 2
37638 is composite. Its prime factorisation is
- 3
The divisors add up to 90720; without 37638 itself that is 53082, so 37638 is abundant (53082 is more than 37638). Euler's totient φ(37638) = 11520 numbers up to 37638 share no factor with it.
- 4
The digits of 37638 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 62 steps to reach 1.
LaTeX source of the formulas on this page
\[ 37638 = 2 \times 3^{3} \times 17 \times 41 \]37638 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 90720 |
| Euler totient φ(n) | 11520 |
| Square | 1416619044 |
| Cube | 53318707578072 |
| Square root | 194.005155 (= 3√4182) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 62 |
| Scientific notation | 3.7638 × |
37638 in other forms
| Form | Value |
|---|---|
| In words | thirty-seven thousand six hundred and thirty-eight |
| Binary (base 2) | 1001001100000110 |
| Octal (base 8) | 111406 |
| Hexadecimal (base 16) | 9306 |
| Base 3 | 1220122000 |
| As time | 37638 seconds = 10 h 27 min 18 s |
Is 37638 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (37638 ÷ 2 = 18819) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (37638 ÷ 3 = 12546) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (37638 ÷ 6 = 6273) | 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 6) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (37638 ÷ 9 = 4182) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 37638 a prime number?
No. 37638 = 2 × × 17 × 41, so it is divisible by 2.
What are the factors of 37638?
1, 2, 3, 6, 9, 17, 18, 27, 34, 41, 51, 54, 82, 102, 123, 153, 246, 306, 369, 459, 697, 738, 918, 1107, 1394, 2091, 2214, 4182, 6273, 12546, 18819, 37638.
What is 37638 in binary?
1001001100000110 (hexadecimal 9306, octal 111406).
What is the square root of 37638?
About 194.0052, exactly 3√4182.
Is 37638 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 37638?
37638 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 27.