The number 13577
13577 is the 1606th prime number. Its only divisors are 1 and 13577.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13577: the 1606th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
13577 is prime, so its only factors are 1 and 13577. It is the 1606th prime; the next prime is 13591 and the one before is 13567.
- 3
The divisors add up to 13578; without 13577 itself that is 1, so 13577 is deficient (1 is less than 13577). Euler's totient φ(13577) = 13576 numbers up to 13577 share no factor with it.
- 4
The digits of 13577 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 89 steps to reach 1.
13577 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 13578 |
| Euler totient φ(n) | 13576 |
| Square | 184334929 |
| Cube | 2502715331033 |
| Square root | 116.520384 |
| Digit sum / digital root | 23 / 5 |
| Collatz steps to 1 | 89 |
| Scientific notation | 1.3577 × |
13577 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand five hundred and seventy-seven |
| Binary (base 2) | 11010100001001 |
| Octal (base 8) | 32411 |
| Hexadecimal (base 16) | 3509 |
| Base 3 | 200121212 |
| As time | 13577 seconds = 3 h 46 min 17 s |
Is 13577 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 2) | 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 4) | 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 7) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 3) | 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 13577 a prime number?
Yes. 13577 is divisible only by 1 and itself.
What are the factors of 13577?
1, 13577.
What is 13577 in binary?
11010100001001 (hexadecimal 3509, octal 32411).
What is the square root of 13577?
About 116.5204.
Is 13577 divisible by 3?
No. Its digits add up to 23, which is not a multiple of 3.
What is special about the number 13577?
13577 is the 1606th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.