The number 727
727 is a palindromic prime: it reads the same backwards and is prime, the 129th prime number and a palindrome: it reads 727 backwards too. Its only divisors are 1 and 727.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 727: a palindromic prime: it reads the same backwards and is prime; the 129th prime number; a palindrome: it reads 727 backwards too.
- 2
727 is prime, so its only factors are 1 and 727. It is the 129th prime; the next prime is 733 and the one before is 719.
- 3
The divisors add up to 728; without 727 itself that is 1, so 727 is deficient (1 is less than 727). Euler's totient φ(727) = 726 numbers up to 727 share no factor with it.
- 4
The digits of 727 add up to 16, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 46 steps to reach 1.
727 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 728 |
| Euler totient φ(n) | 726 |
| Square | 528529 |
| Cube | 384240583 |
| Square root | 26.962938 |
| Digit sum / digital root | 16 / 7 |
| Collatz steps to 1 | 46 |
| Scientific notation | 7.27 × |
727 in other forms
| Form | Value |
|---|---|
| In words | seven hundred and twenty-seven |
| Roman numerals | DCCXXVII |
| Binary (base 2) | 1011010111 |
| Octal (base 8) | 1327 |
| Hexadecimal (base 16) | 2D7 |
| Base 3 | 222221 |
| As time | 727 seconds = 12 min 7 s |
Is 727 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 6) | 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 7) | 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 1) | 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 727 a prime number?
Yes. 727 is divisible only by 1 and itself.
What are the factors of 727?
1, 727.
What is 727 in binary?
1011010111 (hexadecimal 2D7, octal 1327).
What is the square root of 727?
About 26.9629.
What is 727 in Roman numerals?
DCCXXVII.
Is 727 divisible by 3?
No. Its digits add up to 16, which is not a multiple of 3.
What is special about the number 727?
727 is a palindromic prime: it reads the same backwards and is prime; the 129th prime number; a palindrome: it reads 727 backwards too.