The number 59
59 is a twin prime (59 and 61 are both prime) and the 17th prime number. Its only divisors are 1 and 59.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 59: a twin prime (59 and 61 are both prime); the 17th prime number.
- 2
59 is prime, so its only factors are 1 and 59. It is the 17th prime; the next prime is 61 and the one before is 53.
- 3
The divisors add up to 60; without 59 itself that is 1, so 59 is deficient (1 is less than 59). Euler's totient φ(59) = 58 numbers up to 59 share no factor with it.
- 4
The digits of 59 add up to 14, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 32 steps to reach 1.
59 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 60 |
| Euler totient φ(n) | 58 |
| Square | 3481 |
| Cube | 205379 |
| Square root | 7.681146 |
| Digit sum / digital root | 14 / 5 |
| Collatz steps to 1 | 32 |
| Scientific notation | 5.9 × |
59 in other forms
| Form | Value |
|---|---|
| In words | fifty-nine |
| Roman numerals | LIX |
| Binary (base 2) | 111011 |
| Octal (base 8) | 73 |
| Hexadecimal (base 16) | 3B |
| Base 3 | 2012 |
| As time | 59 seconds |
Is 59 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 4) | 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 3) | 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 3) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 5) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 9) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 4) | 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 59 a prime number?
Yes. 59 is divisible only by 1 and itself.
What are the factors of 59?
1, 59.
What is 59 in binary?
111011 (hexadecimal 3B, octal 73).
What is the square root of 59?
About 7.6811.
What is 59 in Roman numerals?
LIX.
Is 59 divisible by 3?
No. Its digits add up to 14, which is not a multiple of 3.
What is special about the number 59?
59 is a twin prime (59 and 61 are both prime); the 17th prime number.