The number 65
65 is a binary palindrome (1000001). Its prime factorisation is 5 × 13. Divisors (4): 1, 5, 13, 65.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 65: a binary palindrome (1000001); a semiprime: 5 × 13, the product of two primes.
- 2
65 is composite. Its prime factorisation is
- 3
The divisors add up to 84; without 65 itself that is 19, so 65 is deficient (19 is less than 65). Euler's totient φ(65) = 48 numbers up to 65 share no factor with it.
- 4
The digits of 65 add up to 11, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 27 steps to reach 1.
LaTeX source of the formulas on this page
\[ 65 = 5 \times 13 \]
65 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 4 |
| Sum of divisors | 84 |
| Euler totient φ(n) | 48 |
| Square | 4225 |
| Cube | 274625 |
| Square root | 8.062258 |
| Digit sum / digital root | 11 / 2 |
| Collatz steps to 1 | 27 |
| Scientific notation | 6.5 × |
65 in other forms
| Form | Value |
|---|---|
| In words | sixty-five |
| Roman numerals | LXV |
| Binary (base 2) | 1000001 |
| Octal (base 8) | 101 |
| Hexadecimal (base 16) | 41 |
| Base 3 | 2102 |
| As time | 65 seconds = 1 min 5 s |
Is 65 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 1) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (65 ÷ 5 = 13) | 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 2) | 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 1) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 2) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 5) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 5) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 65 a prime number?
No. 65 = 5 × 13, so it is divisible by 5.
What are the factors of 65?
1, 5, 13, 65.
What is 65 in binary?
1000001 (hexadecimal 41, octal 101).
What is the square root of 65?
About 8.0623.
What is 65 in Roman numerals?
LXV.
Is 65 divisible by 3?
No. Its digits add up to 11, which is not a multiple of 3.
What is special about the number 65?
65 is a binary palindrome (1000001); a semiprime: 5 × 13, the product of two primes.