The number 13757
13757 is a twin prime (13757 and 13759 are both prime) and the 1627th prime number. Its only divisors are 1 and 13757.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13757: a twin prime (13757 and 13759 are both prime); the 1627th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
13757 is prime, so its only factors are 1 and 13757. It is the 1627th prime; the next prime is 13759 and the one before is 13751.
- 3
The divisors add up to 13758; without 13757 itself that is 1, so 13757 is deficient (1 is less than 13757). Euler's totient φ(13757) = 13756 numbers up to 13757 share no factor with it.
- 4
The digits of 13757 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 151 steps to reach 1.
13757 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 13758 |
| Euler totient φ(n) | 13756 |
| Square | 189255049 |
| Cube | 2603581709093 |
| Square root | 117.290238 |
| Digit sum / digital root | 23 / 5 |
| Collatz steps to 1 | 151 |
| Scientific notation | 1.3757 × |
13757 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand seven hundred and fifty-seven |
| Binary (base 2) | 11010110111101 |
| Octal (base 8) | 32675 |
| Hexadecimal (base 16) | 35BD |
| Base 3 | 200212112 |
| As time | 13757 seconds = 3 h 49 min 17 s |
Is 13757 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 2) | 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 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 7) | 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 13757 a prime number?
Yes. 13757 is divisible only by 1 and itself.
What are the factors of 13757?
1, 13757.
What is 13757 in binary?
11010110111101 (hexadecimal 35BD, octal 32675).
What is the square root of 13757?
About 117.2902.
Is 13757 divisible by 3?
No. Its digits add up to 23, which is not a multiple of 3.
What is special about the number 13757?
13757 is a twin prime (13757 and 13759 are both prime); the 1627th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.