The number 13515
13515 is a binary palindrome (11010011001011). Its prime factorisation is 3 × 5 × 17 × 53. Divisors (16): 1, 3, 5, 15, 17, 51, 53, 85, 159, 255, 265, 795, 901, 2703, 4505, 13515.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13515: a binary palindrome (11010011001011); a Harshad number: divisible by its digit sum 15.
- 2
13515 is composite. Its prime factorisation is
- 3
The divisors add up to 23328; without 13515 itself that is 9813, so 13515 is deficient (9813 is less than 13515). Euler's totient φ(13515) = 6656 numbers up to 13515 share no factor with it.
- 4
The digits of 13515 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 37 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13515 = 3 \times 5 \times 17 \times 53 \]
13515 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 23328 |
| Euler totient φ(n) | 6656 |
| Square | 182655225 |
| Cube | 2468585365875 |
| Square root | 116.254032 |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 37 |
| Scientific notation | 1.3515 × |
13515 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand five hundred and fifteen |
| Binary (base 2) | 11010011001011 |
| Octal (base 8) | 32313 |
| Hexadecimal (base 16) | 34CB |
| Base 3 | 200112120 |
| As time | 13515 seconds = 3 h 45 min 15 s |
Is 13515 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 (13515 ÷ 3 = 4505) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 3) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (13515 ÷ 5 = 2703) | 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 5) | 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 3) | 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 | No (remainder 5) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 3) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13515 a prime number?
No. 13515 = 3 × 5 × 17 × 53, so it is divisible by 3.
What are the factors of 13515?
1, 3, 5, 15, 17, 51, 53, 85, 159, 255, 265, 795, 901, 2703, 4505, 13515.
What is 13515 in binary?
11010011001011 (hexadecimal 34CB, octal 32313).
What is the square root of 13515?
About 116.2540.
Is 13515 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 13515?
13515 is a binary palindrome (11010011001011); a Harshad number: divisible by its digit sum 15.