The number 37680
37680 is a composite number with 40 divisors. Its prime factorisation is × 3 × 5 × 157. Divisors (40): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48 … 37680.
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How to work it out
- 1
What is special about 37680: a Harshad number: divisible by its digit sum 24.
- 2
37680 is composite. Its prime factorisation is
- 3
The divisors add up to 117552; without 37680 itself that is 79872, so 37680 is abundant (79872 is more than 37680). Euler's totient φ(37680) = 9984 numbers up to 37680 share no factor with it.
- 4
The digits of 37680 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 36 steps to reach 1.
LaTeX source of the formulas on this page
\[ 37680 = 2^{4} \times 3 \times 5 \times 157 \]37680 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 117552 |
| Euler totient φ(n) | 9984 |
| Square | 1419782400 |
| Cube | 53497400832000 |
| Square root | 194.113369 (= 4√2355) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 36 |
| Scientific notation | 3.768 × |
37680 in other forms
| Form | Value |
|---|---|
| In words | thirty-seven thousand six hundred and eighty |
| Binary (base 2) | 1001001100110000 |
| Octal (base 8) | 111460 |
| Hexadecimal (base 16) | 9330 |
| Base 3 | 1220200120 |
| As time | 37680 seconds = 10 h 28 min 0 s |
Is 37680 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (37680 ÷ 2 = 18840) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (37680 ÷ 3 = 12560) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (37680 ÷ 4 = 9420) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (37680 ÷ 5 = 7536) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (37680 ÷ 6 = 6280) | 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 | Yes (37680 ÷ 8 = 4710) | 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 | Yes (37680 ÷ 10 = 3768) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (37680 ÷ 12 = 3140) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 37680 a prime number?
No. 37680 = × 3 × 5 × 157, so it is divisible by 2.
What are the factors of 37680?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 157, 240, 314, 471, 628, 785, 942, 1256, 1570, 1884, 2355, 2512, 3140, 3768, 4710, 6280, 7536, 9420, 12560, 18840, 37680.
What is 37680 in binary?
1001001100110000 (hexadecimal 9330, octal 111460).
What is the square root of 37680?
About 194.1134, exactly 4√2355.
Is 37680 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 37680?
37680 is a Harshad number: divisible by its digit sum 24.