The number 37368
37368 is a composite number with 32 divisors. Its prime factorisation is × × 173. Divisors (32): 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 173 … 37368.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 37368: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 27.
- 2
37368 is composite. Its prime factorisation is
- 3
The divisors add up to 104400; without 37368 itself that is 67032, so 37368 is abundant (67032 is more than 37368). Euler's totient φ(37368) = 12384 numbers up to 37368 share no factor with it.
- 4
The digits of 37368 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 93 steps to reach 1.
LaTeX source of the formulas on this page
\[ 37368 = 2^{3} \times 3^{3} \times 173 \]37368 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 104400 |
| Euler totient φ(n) | 12384 |
| Square | 1396367424 |
| Cube | 52179457900032 |
| Square root | 193.308044 (= 6√1038) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 93 |
| Scientific notation | 3.7368 × |
37368 in other forms
| Form | Value |
|---|---|
| In words | thirty-seven thousand three hundred and sixty-eight |
| Binary (base 2) | 1001000111111000 |
| Octal (base 8) | 110770 |
| Hexadecimal (base 16) | 91F8 |
| Base 3 | 1220021000 |
| As time | 37368 seconds = 10 h 22 min 48 s |
Is 37368 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (37368 ÷ 2 = 18684) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (37368 ÷ 3 = 12456) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (37368 ÷ 4 = 9342) | 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 (37368 ÷ 6 = 6228) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 (37368 ÷ 8 = 4671) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (37368 ÷ 9 = 4152) | 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 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (37368 ÷ 12 = 3114) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 37368 a prime number?
No. 37368 = × × 173, so it is divisible by 2.
What are the factors of 37368?
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 173, 216, 346, 519, 692, 1038, 1384, 1557, 2076, 3114, 4152, 4671, 6228, 9342, 12456, 18684, 37368.
What is 37368 in binary?
1001000111111000 (hexadecimal 91F8, octal 110770).
What is the square root of 37368?
About 193.3080, exactly 6√1038.
Is 37368 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 37368?
37368 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 27.