The number 37201
37201 is a twin prime (37199 and 37201 are both prime) and the 3942nd prime number. Its only divisors are 1 and 37201.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 37201: a twin prime (37199 and 37201 are both prime); the 3942nd prime number.
- 2
37201 is prime, so its only factors are 1 and 37201. It is the 3942nd prime; the next prime is 37217 and the one before is 37199.
- 3
The divisors add up to 37202; without 37201 itself that is 1, so 37201 is deficient (1 is less than 37201). Euler's totient φ(37201) = 37200 numbers up to 37201 share no factor with it.
- 4
The digits of 37201 add up to 13, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 137 steps to reach 1.
37201 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 37202 |
| Euler totient φ(n) | 37200 |
| Square | 1383914401 |
| Cube | 51482999631601 |
| Square root | 192.875608 |
| Digit sum / digital root | 13 / 4 |
| Collatz steps to 1 | 137 |
| Scientific notation | 3.7201 × |
37201 in other forms
| Form | Value |
|---|---|
| In words | thirty-seven thousand two hundred and one |
| Binary (base 2) | 1001000101010001 |
| Octal (base 8) | 110521 |
| Hexadecimal (base 16) | 9151 |
| Base 3 | 1220000211 |
| As time | 37201 seconds = 10 h 20 min 1 s |
Is 37201 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 1) | 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 3) | 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 1) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | 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 37201 a prime number?
Yes. 37201 is divisible only by 1 and itself.
What are the factors of 37201?
1, 37201.
What is 37201 in binary?
1001000101010001 (hexadecimal 9151, octal 110521).
What is the square root of 37201?
About 192.8756.
Is 37201 divisible by 3?
No. Its digits add up to 13, which is not a multiple of 3.
What is special about the number 37201?
37201 is a twin prime (37199 and 37201 are both prime); the 3942nd prime number.