The number 13649
13649 is the 1613th prime number. Its only divisors are 1 and 13649.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13649: the 1613th prime number.
- 2
13649 is prime, so its only factors are 1 and 13649. It is the 1613th prime; the next prime is 13669 and the one before is 13633.
- 3
The divisors add up to 13650; without 13649 itself that is 1, so 13649 is deficient (1 is less than 13649). Euler's totient φ(13649) = 13648 numbers up to 13649 share no factor with it.
- 4
The digits of 13649 add up to 23, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 120 steps to reach 1.
13649 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 13650 |
| Euler totient φ(n) | 13648 |
| Square | 186295201 |
| Cube | 2542743198449 |
| Square root | 116.828935 |
| Digit sum / digital root | 23 / 5 |
| Collatz steps to 1 | 120 |
| Scientific notation | 1.3649 × |
13649 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand six hundred and forty-nine |
| Binary (base 2) | 11010101010001 |
| Octal (base 8) | 32521 |
| Hexadecimal (base 16) | 3551 |
| Base 3 | 200201112 |
| As time | 13649 seconds = 3 h 47 min 29 s |
Is 13649 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 | No (remainder 4) | 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 1) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 5) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 9) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | 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 13649 a prime number?
Yes. 13649 is divisible only by 1 and itself.
What are the factors of 13649?
1, 13649.
What is 13649 in binary?
11010101010001 (hexadecimal 3551, octal 32521).
What is the square root of 13649?
About 116.8289.
Is 13649 divisible by 3?
No. Its digits add up to 23, which is not a multiple of 3.
What is special about the number 13649?
13649 is the 1613th prime number.