The number 73
73 is a twin prime (71 and 73 are both prime), the 21st prime number and a binary palindrome (1001001). Its only divisors are 1 and 73.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 73: a twin prime (71 and 73 are both prime); the 21st prime number; a binary palindrome (1001001).
- 2
73 is prime, so its only factors are 1 and 73. It is the 21st prime; the next prime is 79 and the one before is 71.
- 3
The divisors add up to 74; without 73 itself that is 1, so 73 is deficient (1 is less than 73). Euler's totient φ(73) = 72 numbers up to 73 share no factor with it.
- 4
The digits of 73 add up to 10, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 115 steps to reach 1.
73 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 74 |
| Euler totient φ(n) | 72 |
| Square | 5329 |
| Cube | 389017 |
| Square root | 8.544004 |
| Digit sum / digital root | 10 / 1 |
| Collatz steps to 1 | 115 |
| Scientific notation | 7.3 × |
73 in other forms
| Form | Value |
|---|---|
| In words | seventy-three |
| Roman numerals | LXXIII |
| Binary (base 2) | 1001001 |
| Octal (base 8) | 111 |
| Hexadecimal (base 16) | 49 |
| Base 3 | 2201 |
| As time | 73 seconds = 1 min 13 s |
Is 73 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 3) | 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 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 1) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 1) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 3) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | 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 73 a prime number?
Yes. 73 is divisible only by 1 and itself.
What are the factors of 73?
1, 73.
What is 73 in binary?
1001001 (hexadecimal 49, octal 111).
What is the square root of 73?
About 8.5440.
What is 73 in Roman numerals?
LXXIII.
Is 73 divisible by 3?
No. Its digits add up to 10, which is not a multiple of 3.
What is special about the number 73?
73 is a twin prime (71 and 73 are both prime); the 21st prime number; a binary palindrome (1001001).