The number 137
137 is a twin prime (137 and 139 are both prime) and the 33rd prime number. Its only divisors are 1 and 137.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 137: a twin prime (137 and 139 are both prime); the 33rd prime number.
- 2
137 is prime, so its only factors are 1 and 137. It is the 33rd prime; the next prime is 139 and the one before is 131.
- 3
The divisors add up to 138; without 137 itself that is 1, so 137 is deficient (1 is less than 137). Euler's totient φ(137) = 136 numbers up to 137 share no factor with it.
- 4
The digits of 137 add up to 11, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 90 steps to reach 1.
137 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 138 |
| Euler totient φ(n) | 136 |
| Square | 18769 |
| Cube | 2571353 |
| Square root | 11.704700 |
| Digit sum / digital root | 11 / 2 |
| Collatz steps to 1 | 90 |
| Scientific notation | 1.37 × |
137 in other forms
| Form | Value |
|---|---|
| In words | one hundred and thirty-seven |
| Roman numerals | CXXXVII |
| Binary (base 2) | 10001001 |
| Octal (base 8) | 211 |
| Hexadecimal (base 16) | 89 |
| Base 3 | 12002 |
| As time | 137 seconds = 2 min 17 s |
Is 137 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 2) | 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 5) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 2) | 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 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 5) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 137 a prime number?
Yes. 137 is divisible only by 1 and itself.
What are the factors of 137?
1, 137.
What is 137 in binary?
10001001 (hexadecimal 89, octal 211).
What is the square root of 137?
About 11.7047.
What is 137 in Roman numerals?
CXXXVII.
Is 137 divisible by 3?
No. Its digits add up to 11, which is not a multiple of 3.
What is special about the number 137?
137 is a twin prime (137 and 139 are both prime); the 33rd prime number.