The number 10125
10125 is a composite number with 20 divisors. Its prime factorisation is × . Divisors (20): 1, 3, 5, 9, 15, 25, 27, 45, 75, 81, 125, 135, 225, 375, 405, 675 … 10125.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 10125: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.
- 2
10125 is composite. Its prime factorisation is
- 3
The divisors add up to 18876; without 10125 itself that is 8751, so 10125 is deficient (8751 is less than 10125). Euler's totient φ(10125) = 5400 numbers up to 10125 share no factor with it.
- 4
The digits of 10125 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 42 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10125 = 3^{4} \times 5^{3} \]10125 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 18876 |
| Euler totient φ(n) | 5400 |
| Square | 102515625 |
| Cube | 1037970703125 |
| Square root | 100.623059 (= 45√5) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 42 |
| Scientific notation | 1.0125 × |
10125 in other forms
| Form | Value |
|---|---|
| In words | ten thousand one hundred and twenty-five |
| Binary (base 2) | 10011110001101 |
| Octal (base 8) | 23615 |
| Hexadecimal (base 16) | 278D |
| Base 3 | 111220000 |
| As time | 10125 seconds = 2 h 48 min 45 s |
Is 10125 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 (10125 ÷ 3 = 3375) | 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 (10125 ÷ 5 = 2025) | 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 | Yes (10125 ÷ 9 = 1125) | 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 5) | 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 10125 a prime number?
No. 10125 = × , so it is divisible by 3.
What are the factors of 10125?
1, 3, 5, 9, 15, 25, 27, 45, 75, 81, 125, 135, 225, 375, 405, 675, 1125, 2025, 3375, 10125.
What is 10125 in binary?
10011110001101 (hexadecimal 278D, octal 23615).
What is the square root of 10125?
About 100.6231, exactly 45√5.
Is 10125 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 10125?
10125 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.