The number 73973
73973 is the 7300th prime number. Its only divisors are 1 and 73973.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 73973: the 7300th prime number.
- 2
73973 is prime, so its only factors are 1 and 73973. It is the 7300th prime; the next prime is 73999 and the one before is 73961.
- 3
The divisors add up to 73974; without 73973 itself that is 1, so 73973 is deficient (1 is less than 73973). Euler's totient φ(73973) = 73972 numbers up to 73973 share no factor with it.
- 4
The digits of 73973 add up to 29, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 156 steps to reach 1.
73973 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 73974 |
| Euler totient φ(n) | 73972 |
| Square | 5472004729 |
| Cube | 404780605818317 |
| Square root | 271.979779 |
| Digit sum / digital root | 29 / 2 |
| Collatz steps to 1 | 156 |
| Scientific notation | 7.3973 × |
73973 in other forms
| Form | Value |
|---|---|
| In words | seventy-three thousand nine hundred and seventy-three |
| Binary (base 2) | 10010000011110101 |
| Octal (base 8) | 220365 |
| Hexadecimal (base 16) | 120F5 |
| Base 3 | 10202110202 |
| As time | 73973 seconds = 20 h 32 min 53 s |
Is 73973 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 | No (remainder 3) | 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 4) | 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 2) | 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 9) | 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 73973 a prime number?
Yes. 73973 is divisible only by 1 and itself.
What are the factors of 73973?
1, 73973.
What is 73973 in binary?
10010000011110101 (hexadecimal 120F5, octal 220365).
What is the square root of 73973?
About 271.9798.
Is 73973 divisible by 3?
No. Its digits add up to 29, which is not a multiple of 3.
What is special about the number 73973?
73973 is the 7300th prime number.