The number 2137
2137 is the 322nd prime number. Its only divisors are 1 and 2137.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 2137: the 322nd prime number.
- 2
2137 is prime, so its only factors are 1 and 2137. It is the 322nd prime; the next prime is 2141 and the one before is 2131.
- 3
The divisors add up to 2138; without 2137 itself that is 1, so 2137 is deficient (1 is less than 2137). Euler's totient φ(2137) = 2136 numbers up to 2137 share no factor with it.
- 4
The digits of 2137 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 63 steps to reach 1.
2137 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 2138 |
| Euler totient φ(n) | 2136 |
| Square | 4566769 |
| Cube | 9759185353 |
| Square root | 46.227697 |
| Digit sum / digital root | 13 / 4 |
| Collatz steps to 1 | 63 |
| Scientific notation | 2.137 × |
2137 in other forms
| Form | Value |
|---|---|
| In words | two thousand one hundred and thirty-seven |
| Roman numerals | MMCXXXVII |
| Binary (base 2) | 100001011001 |
| Octal (base 8) | 4131 |
| Hexadecimal (base 16) | 859 |
| Base 3 | 2221011 |
| As time | 2137 seconds = 35 min 37 s |
Is 2137 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 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 2137 a prime number?
Yes. 2137 is divisible only by 1 and itself.
What are the factors of 2137?
1, 2137.
What is 2137 in binary?
100001011001 (hexadecimal 859, octal 4131).
What is the square root of 2137?
About 46.2277.
What is 2137 in Roman numerals?
MMCXXXVII.
Is 2137 divisible by 3?
No. Its digits add up to 13, which is not a multiple of 3.
What is special about the number 2137?
2137 is the 322nd prime number.