The number 37104
37104 is a composite number with 20 divisors. Its prime factorisation is × 3 × 773. Divisors (20): 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 773, 1546, 2319, 3092, 4638, 6184 … 37104.
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How to work it out
- 1
37104 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
37104 is composite. Its prime factorisation is
- 3
The divisors add up to 95976; without 37104 itself that is 58872, so 37104 is abundant (58872 is more than 37104). Euler's totient φ(37104) = 12352 numbers up to 37104 share no factor with it.
- 4
The digits of 37104 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 62 steps to reach 1.
LaTeX source of the formulas on this page
\[ 37104 = 2^{4} \times 3 \times 773 \]37104 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 95976 |
| Euler totient φ(n) | 12352 |
| Square | 1376706816 |
| Cube | 51081329700864 |
| Square root | 192.623986 (= 4√2319) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 62 |
| Scientific notation | 3.7104 × |
37104 in other forms
| Form | Value |
|---|---|
| In words | thirty-seven thousand one hundred and four |
| Binary (base 2) | 1001000011110000 |
| Octal (base 8) | 110360 |
| Hexadecimal (base 16) | 90F0 |
| Base 3 | 1212220020 |
| As time | 37104 seconds = 10 h 18 min 24 s |
Is 37104 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (37104 ÷ 2 = 18552) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (37104 ÷ 3 = 12368) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (37104 ÷ 4 = 9276) | 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 | Yes (37104 ÷ 6 = 6184) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 (37104 ÷ 8 = 4638) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | 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 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (37104 ÷ 12 = 3092) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 37104 a prime number?
No. 37104 = × 3 × 773, so it is divisible by 2.
What are the factors of 37104?
1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 773, 1546, 2319, 3092, 4638, 6184, 9276, 12368, 18552, 37104.
What is 37104 in binary?
1001000011110000 (hexadecimal 90F0, octal 110360).
What is the square root of 37104?
About 192.6240, exactly 4√2319.
Is 37104 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 37104?
It is a composite number with 20 divisors.