The number 19937
19937 is the 2254th prime number. Its only divisors are 1 and 19937.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 19937: the 2254th prime number.
- 2
19937 is prime, so its only factors are 1 and 19937. It is the 2254th prime; the next prime is 19949 and the one before is 19927.
- 3
The divisors add up to 19938; without 19937 itself that is 1, so 19937 is deficient (1 is less than 19937). Euler's totient φ(19937) = 19936 numbers up to 19937 share no factor with it.
- 4
The digits of 19937 add up to 29, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 74 steps to reach 1.
19937 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 19938 |
| Euler totient φ(n) | 19936 |
| Square | 397483969 |
| Cube | 7924637889953 |
| Square root | 141.198442 |
| Digit sum / digital root | 29 / 2 |
| Collatz steps to 1 | 74 |
| Scientific notation | 1.9937 × |
19937 in other forms
| Form | Value |
|---|---|
| In words | nineteen thousand nine hundred and thirty-seven |
| Binary (base 2) | 100110111100001 |
| Octal (base 8) | 46741 |
| Hexadecimal (base 16) | 4DE1 |
| Base 3 | 1000100102 |
| As time | 19937 seconds = 5 h 32 min 17 s |
Is 19937 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 1) | 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 2) | 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 5) | 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 19937 a prime number?
Yes. 19937 is divisible only by 1 and itself.
What are the factors of 19937?
1, 19937.
What is 19937 in binary?
100110111100001 (hexadecimal 4DE1, octal 46741).
What is the square root of 19937?
About 141.1984.
Is 19937 divisible by 3?
No. Its digits add up to 29, which is not a multiple of 3.
What is special about the number 19937?
19937 is the 2254th prime number.