The number 21937
21937 is the 2459th prime number. Its only divisors are 1 and 21937.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 21937: the 2459th prime number.
- 2
21937 is prime, so its only factors are 1 and 21937. It is the 2459th prime; the next prime is 21943 and the one before is 21929.
- 3
The divisors add up to 21938; without 21937 itself that is 1, so 21937 is deficient (1 is less than 21937). Euler's totient φ(21937) = 21936 numbers up to 21937 share no factor with it.
- 4
The digits of 21937 add up to 22, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 43 steps to reach 1.
21937 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 21938 |
| Euler totient φ(n) | 21936 |
| Square | 481231969 |
| Cube | 10556785703953 |
| Square root | 148.111445 |
| Digit sum / digital root | 22 / 4 |
| Collatz steps to 1 | 43 |
| Scientific notation | 2.1937 × |
21937 in other forms
| Form | Value |
|---|---|
| In words | twenty-one thousand nine hundred and thirty-seven |
| Binary (base 2) | 101010110110001 |
| Octal (base 8) | 52661 |
| Hexadecimal (base 16) | 55B1 |
| Base 3 | 1010002111 |
| As time | 21937 seconds = 6 h 5 min 37 s |
Is 21937 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 1) | 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 1) | 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 4) | 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 1) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 21937 a prime number?
Yes. 21937 is divisible only by 1 and itself.
What are the factors of 21937?
1, 21937.
What is 21937 in binary?
101010110110001 (hexadecimal 55B1, octal 52661).
What is the square root of 21937?
About 148.1114.
Is 21937 divisible by 3?
No. Its digits add up to 22, which is not a multiple of 3.
What is special about the number 21937?
21937 is the 2459th prime number.