The number 9973
9973 is the 1229th prime number. Its only divisors are 1 and 9973.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 9973: the 1229th prime number.
- 2
9973 is prime, so its only factors are 1 and 9973. It is the 1229th prime; the next prime is 10007 and the one before is 9967.
- 3
The divisors add up to 9974; without 9973 itself that is 1, so 9973 is deficient (1 is less than 9973). Euler's totient φ(9973) = 9972 numbers up to 9973 share no factor with it.
- 4
The digits of 9973 add up to 28, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 135 steps to reach 1.
9973 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 9974 |
| Euler totient φ(n) | 9972 |
| Square | 99460729 |
| Cube | 991921850317 |
| Square root | 99.864909 |
| Digit sum / digital root | 28 / 1 |
| Collatz steps to 1 | 135 |
| Scientific notation | 9.973 × |
9973 in other forms
| Form | Value |
|---|---|
| In words | nine thousand nine hundred and seventy-three |
| Binary (base 2) | 10011011110101 |
| Octal (base 8) | 23365 |
| Hexadecimal (base 16) | 26F5 |
| Base 3 | 111200101 |
| As time | 9973 seconds = 2 h 46 min 13 s |
Is 9973 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 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 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 9973 a prime number?
Yes. 9973 is divisible only by 1 and itself.
What are the factors of 9973?
1, 9973.
What is 9973 in binary?
10011011110101 (hexadecimal 26F5, octal 23365).
What is the square root of 9973?
About 99.8649.
Is 9973 divisible by 3?
No. Its digits add up to 28, which is not a multiple of 3.
What is special about the number 9973?
9973 is the 1229th prime number.