The number 9967
9967 is the 1228th prime number. Its only divisors are 1 and 9967.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 9967: the 1228th prime number.
- 2
9967 is prime, so its only factors are 1 and 9967. It is the 1228th prime; the next prime is 9973 and the one before is 9949.
- 3
The divisors add up to 9968; without 9967 itself that is 1, so 9967 is deficient (1 is less than 9967). Euler's totient φ(9967) = 9966 numbers up to 9967 share no factor with it.
- 4
The digits of 9967 add up to 31, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 73 steps to reach 1.
9967 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 9968 |
| Euler totient φ(n) | 9966 |
| Square | 99341089 |
| Cube | 990132634063 |
| Square root | 99.834864 |
| Digit sum / digital root | 31 / 4 |
| Collatz steps to 1 | 73 |
| Scientific notation | 9.967 × |
9967 in other forms
| Form | Value |
|---|---|
| In words | nine thousand nine hundred and sixty-seven |
| Binary (base 2) | 10011011101111 |
| Octal (base 8) | 23357 |
| Hexadecimal (base 16) | 26EF |
| Base 3 | 111200011 |
| As time | 9967 seconds = 2 h 46 min 7 s |
Is 9967 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 3) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | 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 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 7) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 4) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 7) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 7) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 9967 a prime number?
Yes. 9967 is divisible only by 1 and itself.
What are the factors of 9967?
1, 9967.
What is 9967 in binary?
10011011101111 (hexadecimal 26EF, octal 23357).
What is the square root of 9967?
About 99.8349.
Is 9967 divisible by 3?
No. Its digits add up to 31, which is not a multiple of 3.
What is special about the number 9967?
9967 is the 1228th prime number.