The number 127
127 is a Mersenne prime ( − 1), the 31st prime number and a binary palindrome (1111111). Its only divisors are 1 and 127.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 127: a Mersenne prime ( − 1); the 31st prime number; a binary palindrome (1111111).
- 2
127 is prime, so its only factors are 1 and 127. It is the 31st prime; the next prime is 131 and the one before is 113.
- 3
The divisors add up to 128; without 127 itself that is 1, so 127 is deficient (1 is less than 127). Euler's totient φ(127) = 126 numbers up to 127 share no factor with it.
- 4
The digits of 127 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 46 steps to reach 1.
127 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 128 |
| Euler totient φ(n) | 126 |
| Square | 16129 |
| Cube | 2048383 |
| Square root | 11.269428 |
| Digit sum / digital root | 10 / 1 |
| Collatz steps to 1 | 46 |
| Scientific notation | 1.27 × |
127 in other forms
| Form | Value |
|---|---|
| In words | one hundred and twenty-seven |
| Roman numerals | CXXVII |
| Binary (base 2) | 1111111 |
| Octal (base 8) | 177 |
| Hexadecimal (base 16) | 7F |
| Base 3 | 11201 |
| As time | 127 seconds = 2 min 7 s |
Is 127 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 3) | 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 1) | 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 7) | 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 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 7) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 127 a prime number?
Yes. 127 is divisible only by 1 and itself.
What are the factors of 127?
1, 127.
What is 127 in binary?
1111111 (hexadecimal 7F, octal 177).
What is the square root of 127?
About 11.2694.
What is 127 in Roman numerals?
CXXVII.
Is 127 divisible by 3?
No. Its digits add up to 10, which is not a multiple of 3.
What is special about the number 127?
127 is a Mersenne prime ( − 1); the 31st prime number; a binary palindrome (1111111).