The number 31125
31125 is a triangular number: 1 + 2 + … + 249 = 31125. Its prime factorisation is 3 × × 83. Divisors (16): 1, 3, 5, 15, 25, 75, 83, 125, 249, 375, 415, 1245, 2075, 6225, 10375, 31125.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 31125: a triangular number: 1 + 2 + … + 249 = 31125.
- 2
31125 is composite. Its prime factorisation is
- 3
The divisors add up to 52416; without 31125 itself that is 21291, so 31125 is deficient (21291 is less than 31125). Euler's totient φ(31125) = 16400 numbers up to 31125 share no factor with it.
- 4
The digits of 31125 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 41 steps to reach 1.
LaTeX source of the formulas on this page
\[ 31125 = 3 \times 5^{3} \times 83 \]31125 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 52416 |
| Euler totient φ(n) | 16400 |
| Square | 968765625 |
| Cube | 30152830078125 |
| Square root | 176.422788 (= 5√1245) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 41 |
| Scientific notation | 3.1125 × |
31125 in other forms
| Form | Value |
|---|---|
| In words | thirty-one thousand one hundred and twenty-five |
| Binary (base 2) | 111100110010101 |
| Octal (base 8) | 74625 |
| Hexadecimal (base 16) | 7995 |
| Base 3 | 1120200210 |
| As time | 31125 seconds = 8 h 38 min 45 s |
Is 31125 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (31125 ÷ 3 = 10375) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 1) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (31125 ÷ 5 = 6225) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 3) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 5) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 5) | 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 9) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 31125 a prime number?
No. 31125 = 3 × × 83, so it is divisible by 3.
What are the factors of 31125?
1, 3, 5, 15, 25, 75, 83, 125, 249, 375, 415, 1245, 2075, 6225, 10375, 31125.
What is 31125 in binary?
111100110010101 (hexadecimal 7995, octal 74625).
What is the square root of 31125?
About 176.4228, exactly 5√1245.
Is 31125 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 31125?
31125 is a triangular number: 1 + 2 + … + 249 = 31125.