The number 37890
37890 is a composite number with 24 divisors. Its prime factorisation is 2 × × 5 × 421. Divisors (24): 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90, 421, 842, 1263, 2105 … 37890.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 37890: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
37890 is composite. Its prime factorisation is
- 3
The divisors add up to 98748; without 37890 itself that is 60858, so 37890 is abundant (60858 is more than 37890). Euler's totient φ(37890) = 10080 numbers up to 37890 share no factor with it.
- 4
The digits of 37890 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
\[ 37890 = 2 \times 3^{2} \times 5 \times 421 \]37890 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 98748 |
| Euler totient φ(n) | 10080 |
| Square | 1435652100 |
| Cube | 54396858069000 |
| Square root | 194.653538 (= 3√4210) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 93 |
| Scientific notation | 3.789 × |
37890 in other forms
| Form | Value |
|---|---|
| In words | thirty-seven thousand eight hundred and ninety |
| Binary (base 2) | 1001010000000010 |
| Octal (base 8) | 112002 |
| Hexadecimal (base 16) | 9402 |
| Base 3 | 1220222100 |
| As time | 37890 seconds = 10 h 31 min 30 s |
Is 37890 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (37890 ÷ 2 = 18945) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (37890 ÷ 3 = 12630) | 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 | Yes (37890 ÷ 5 = 7578) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (37890 ÷ 6 = 6315) | 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 2) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (37890 ÷ 9 = 4210) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (37890 ÷ 10 = 3789) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | 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 37890 a prime number?
No. 37890 = 2 × × 5 × 421, so it is divisible by 2.
What are the factors of 37890?
1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90, 421, 842, 1263, 2105, 2526, 3789, 4210, 6315, 7578, 12630, 18945, 37890.
What is 37890 in binary?
1001010000000010 (hexadecimal 9402, octal 112002).
What is the square root of 37890?
About 194.6535, exactly 3√4210.
Is 37890 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 37890?
37890 is a happy number: repeatedly adding the squares of its digits reaches 1.