The number 37500
37500 is a composite number with 36 divisors. Its prime factorisation is × 3 × . Divisors (36): 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100 … 37500.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 37500: a Harshad number: divisible by its digit sum 15.
- 2
37500 is composite. Its prime factorisation is
- 3
The divisors add up to 109368; without 37500 itself that is 71868, so 37500 is abundant (71868 is more than 37500). Euler's totient φ(37500) = 10000 numbers up to 37500 share no factor with it.
- 4
The digits of 37500 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 49 steps to reach 1.
LaTeX source of the formulas on this page
\[ 37500 = 2^{2} \times 3 \times 5^{5} \]37500 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 109368 |
| Euler totient φ(n) | 10000 |
| Square | 1406250000 |
| Cube | 52734375000000 |
| Square root | 193.649167 (= 50√15) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 49 |
| Scientific notation | 3.75 × |
37500 in other forms
| Form | Value |
|---|---|
| In words | thirty-seven thousand five hundred |
| Binary (base 2) | 1001001001111100 |
| Octal (base 8) | 111174 |
| Hexadecimal (base 16) | 927C |
| Base 3 | 1220102220 |
| As time | 37500 seconds = 10 h 25 min 0 s |
Is 37500 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (37500 ÷ 2 = 18750) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (37500 ÷ 3 = 12500) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (37500 ÷ 4 = 9375) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (37500 ÷ 5 = 7500) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (37500 ÷ 6 = 6250) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 4) | 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 (37500 ÷ 10 = 3750) | 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 (37500 ÷ 12 = 3125) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 37500 a prime number?
No. 37500 = × 3 × , so it is divisible by 2.
What are the factors of 37500?
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 125, 150, 250, 300, 375, 500, 625, 750, 1250, 1500, 1875, 2500, 3125, 3750, 6250, 7500, 9375, 12500, 18750, 37500.
What is 37500 in binary?
1001001001111100 (hexadecimal 927C, octal 111174).
What is the square root of 37500?
About 193.6492, exactly 50√15.
Is 37500 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 37500?
37500 is a Harshad number: divisible by its digit sum 15.