The number 71
71 is a twin prime (71 and 73 are both prime) and the 20th prime number. Its only divisors are 1 and 71.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 71: a twin prime (71 and 73 are both prime); the 20th prime number.
- 2
71 is prime, so its only factors are 1 and 71. It is the 20th prime; the next prime is 73 and the one before is 67.
- 3
The divisors add up to 72; without 71 itself that is 1, so 71 is deficient (1 is less than 71). Euler's totient φ(71) = 70 numbers up to 71 share no factor with it.
- 4
The digits of 71 add up to 8, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 102 steps to reach 1.
71 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 72 |
| Euler totient φ(n) | 70 |
| Square | 5041 |
| Cube | 357911 |
| Square root | 8.426150 |
| Digit sum / digital root | 8 / 8 |
| Collatz steps to 1 | 102 |
| Scientific notation | 7.1 × |
71 in other forms
| Form | Value |
|---|---|
| In words | seventy-one |
| Roman numerals | LXXI |
| Binary (base 2) | 1000111 |
| Octal (base 8) | 107 |
| Hexadecimal (base 16) | 47 |
| Base 3 | 2122 |
| As time | 71 seconds = 1 min 11 s |
Is 71 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 3) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | 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 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 8) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 1) | 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 11) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 71 a prime number?
Yes. 71 is divisible only by 1 and itself.
What are the factors of 71?
1, 71.
What is 71 in binary?
1000111 (hexadecimal 47, octal 107).
What is the square root of 71?
About 8.4261.
What is 71 in Roman numerals?
LXXI.
Is 71 divisible by 3?
No. Its digits add up to 8, which is not a multiple of 3.
What is special about the number 71?
71 is a twin prime (71 and 73 are both prime); the 20th prime number.