The number 13125
13125 is a composite number with 20 divisors. Its prime factorisation is 3 × × 7. Divisors (20): 1, 3, 5, 7, 15, 21, 25, 35, 75, 105, 125, 175, 375, 525, 625, 875 … 13125.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
13125 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
13125 is composite. Its prime factorisation is
- 3
The divisors add up to 24992; without 13125 itself that is 11867, so 13125 is deficient (11867 is less than 13125). Euler's totient φ(13125) = 6000 numbers up to 13125 share no factor with it.
- 4
The digits of 13125 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 76 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13125 = 3 \times 5^{4} \times 7 \]13125 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 24992 |
| Euler totient φ(n) | 6000 |
| Square | 172265625 |
| Cube | 2260986328125 |
| Square root | 114.564392 (= 25√21) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 76 |
| Scientific notation | 1.3125 × |
13125 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand one hundred and twenty-five |
| Binary (base 2) | 11001101000101 |
| Octal (base 8) | 31505 |
| Hexadecimal (base 16) | 3345 |
| Base 3 | 200000010 |
| As time | 13125 seconds = 3 h 38 min 45 s |
Is 13125 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 (13125 ÷ 3 = 4375) | 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 (13125 ÷ 5 = 2625) | 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 | Yes (13125 ÷ 7 = 1875) | 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 2) | 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 13125 a prime number?
No. 13125 = 3 × × 7, so it is divisible by 3.
What are the factors of 13125?
1, 3, 5, 7, 15, 21, 25, 35, 75, 105, 125, 175, 375, 525, 625, 875, 1875, 2625, 4375, 13125.
What is 13125 in binary?
11001101000101 (hexadecimal 3345, octal 31505).
What is the square root of 13125?
About 114.5644, exactly 25√21.
Is 13125 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 13125?
It is a composite number with 20 divisors.