The number 61
61 is a twin prime (59 and 61 are both prime) and the 18th prime number. Its only divisors are 1 and 61.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 61: a twin prime (59 and 61 are both prime); the 18th prime number.
- 2
61 is prime, so its only factors are 1 and 61. It is the 18th prime; the next prime is 67 and the one before is 59.
- 3
The divisors add up to 62; without 61 itself that is 1, so 61 is deficient (1 is less than 61). Euler's totient φ(61) = 60 numbers up to 61 share no factor with it.
- 4
The digits of 61 add up to 7, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 19 steps to reach 1.
61 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 62 |
| Euler totient φ(n) | 60 |
| Square | 3721 |
| Cube | 226981 |
| Square root | 7.810250 |
| Digit sum / digital root | 7 / 7 |
| Collatz steps to 1 | 19 |
| Scientific notation | 6.1 × |
61 in other forms
| Form | Value |
|---|---|
| In words | sixty-one |
| Roman numerals | LXI |
| Binary (base 2) | 111101 |
| Octal (base 8) | 75 |
| Hexadecimal (base 16) | 3D |
| Base 3 | 2021 |
| As time | 61 seconds = 1 min 1 s |
Is 61 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 1) | 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 1) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 5) | 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 1) | 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 1) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 61 a prime number?
Yes. 61 is divisible only by 1 and itself.
What are the factors of 61?
1, 61.
What is 61 in binary?
111101 (hexadecimal 3D, octal 75).
What is the square root of 61?
About 7.8102.
What is 61 in Roman numerals?
LXI.
Is 61 divisible by 3?
No. Its digits add up to 7, which is not a multiple of 3.
What is special about the number 61?
61 is a twin prime (59 and 61 are both prime); the 18th prime number.