The number 37813
37813 is a twin prime (37811 and 37813 are both prime) and the 4000th prime number. Its only divisors are 1 and 37813.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 37813: a twin prime (37811 and 37813 are both prime); the 4000th prime number.
- 2
37813 is prime, so its only factors are 1 and 37813. It is the 4000th prime; the next prime is 37831 and the one before is 37811.
- 3
The divisors add up to 37814; without 37813 itself that is 1, so 37813 is deficient (1 is less than 37813). Euler's totient φ(37813) = 37812 numbers up to 37813 share no factor with it.
- 4
The digits of 37813 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 62 steps to reach 1.
37813 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 37814 |
| Euler totient φ(n) | 37812 |
| Square | 1429822969 |
| Cube | 54065895926797 |
| Square root | 194.455650 |
| Digit sum / digital root | 22 / 4 |
| Collatz steps to 1 | 62 |
| Scientific notation | 3.7813 × |
37813 in other forms
| Form | Value |
|---|---|
| In words | thirty-seven thousand eight hundred and thirteen |
| Binary (base 2) | 1001001110110101 |
| Octal (base 8) | 111665 |
| Hexadecimal (base 16) | 93B5 |
| Base 3 | 1220212111 |
| As time | 37813 seconds = 10 h 30 min 13 s |
Is 37813 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 3) | 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 5) | 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 3) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | 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 37813 a prime number?
Yes. 37813 is divisible only by 1 and itself.
What are the factors of 37813?
1, 37813.
What is 37813 in binary?
1001001110110101 (hexadecimal 93B5, octal 111665).
What is the square root of 37813?
About 194.4557.
Is 37813 divisible by 3?
No. Its digits add up to 22, which is not a multiple of 3.
What is special about the number 37813?
37813 is a twin prime (37811 and 37813 are both prime); the 4000th prime number.