The number 37
37 is the 12th prime number. Its only divisors are 1 and 37.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 37: the 12th prime number.
- 2
37 is prime, so its only factors are 1 and 37. It is the 12th prime; the next prime is 41 and the one before is 31.
- 3
The divisors add up to 38; without 37 itself that is 1, so 37 is deficient (1 is less than 37). Euler's totient φ(37) = 36 numbers up to 37 share no factor with it.
- 4
The digits of 37 add up to 10, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 21 steps to reach 1.
37 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 38 |
| Euler totient φ(n) | 36 |
| Square | 1369 |
| Cube | 50653 |
| Square root | 6.082763 |
| Digit sum / digital root | 10 / 1 |
| Collatz steps to 1 | 21 |
| Scientific notation | 3.7 × |
37 in other forms
| Form | Value |
|---|---|
| In words | thirty-seven |
| Roman numerals | XXXVII |
| Binary (base 2) | 100101 |
| Octal (base 8) | 45 |
| Hexadecimal (base 16) | 25 |
| Base 3 | 1101 |
| As time | 37 seconds |
Is 37 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 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 1) | 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 4) | 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 37 a prime number?
Yes. 37 is divisible only by 1 and itself.
What are the factors of 37?
1, 37.
What is 37 in binary?
100101 (hexadecimal 25, octal 45).
What is the square root of 37?
About 6.0828.
What is 37 in Roman numerals?
XXXVII.
Is 37 divisible by 3?
No. Its digits add up to 10, which is not a multiple of 3.
What is special about the number 37?
37 is the 12th prime number.