The number 1973
1973 is the 298th prime number. Its only divisors are 1 and 1973.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1973: the 298th prime number.
- 2
1973 is prime, so its only factors are 1 and 1973. It is the 298th prime; the next prime is 1979 and the one before is 1951.
- 3
The divisors add up to 1974; without 1973 itself that is 1, so 1973 is deficient (1 is less than 1973). Euler's totient φ(1973) = 1972 numbers up to 1973 share no factor with it.
- 4
The digits of 1973 add up to 20, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 50 steps to reach 1.
1973 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 1974 |
| Euler totient φ(n) | 1972 |
| Square | 3892729 |
| Cube | 7680354317 |
| Square root | 44.418465 |
| Digit sum / digital root | 20 / 2 |
| Collatz steps to 1 | 50 |
| Scientific notation | 1.973 × |
1973 in other forms
| Form | Value |
|---|---|
| In words | one thousand nine hundred and seventy-three |
| Roman numerals | MCMLXXIII |
| Binary (base 2) | 11110110101 |
| Octal (base 8) | 3665 |
| Hexadecimal (base 16) | 7B5 |
| Base 3 | 2201002 |
| As time | 1973 seconds = 32 min 53 s |
Is 1973 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 6) | 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 4) | 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 1973 a prime number?
Yes. 1973 is divisible only by 1 and itself.
What are the factors of 1973?
1, 1973.
What is 1973 in binary?
11110110101 (hexadecimal 7B5, octal 3665).
What is the square root of 1973?
About 44.4185.
What is 1973 in Roman numerals?
MCMLXXIII.
Is 1973 divisible by 3?
No. Its digits add up to 20, which is not a multiple of 3.
What is special about the number 1973?
1973 is the 298th prime number.