The number 125
125 is a perfect cube (). Its prime factorisation is . Divisors (4): 1, 5, 25, 125.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 125: a perfect cube ().
- 2
125 is composite. Its prime factorisation is
- 3
The divisors add up to 156; without 125 itself that is 31, so 125 is deficient (31 is less than 125). Euler's totient ฯ(125) = 100 numbers up to 125 share no factor with it.
- 4
The digits of 125 add up to 8, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 108 steps to reach 1.
LaTeX source of the formulas on this page
\[ 125 = 5^{3} \]125 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 4 |
| Sum of divisors | 156 |
| Euler totient ฯ(n) | 100 |
| Square | 15625 |
| Cube | 1953125 |
| Square root | 11.180340 (= 5โ5) |
| Digit sum / digital root | 8 / 8 |
| Collatz steps to 1 | 108 |
| Scientific notation | 1.25 ร |
| Perfect power |
125 in other forms
| Form | Value |
|---|---|
| In words | one hundred and twenty-five |
| Roman numerals | CXXV |
| Binary (base 2) | 1111101 |
| Octal (base 8) | 175 |
| Hexadecimal (base 16) | 7D |
| Base 3 | 11122 |
| As time | 125 seconds = 2 min 5 s |
Is 125 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 | No (remainder 2) | 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 (125 รท 5 = 25) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 5) | 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 5) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 8) | 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 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 5) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 125 a prime number?
No. 125 = , so it is divisible by 5.
What are the factors of 125?
1, 5, 25, 125.
What is 125 in binary?
1111101 (hexadecimal 7D, octal 175).
What is the square root of 125?
About 11.1803, exactly 5โ5.
What is 125 in Roman numerals?
CXXV.
Is 125 divisible by 3?
No. Its digits add up to 8, which is not a multiple of 3.
What is special about the number 125?
125 is a perfect cube ().