The number 967
967 is the 163rd prime number. Its only divisors are 1 and 967.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 967: the 163rd prime number.
- 2
967 is prime, so its only factors are 1 and 967. It is the 163rd prime; the next prime is 971 and the one before is 953.
- 3
The divisors add up to 968; without 967 itself that is 1, so 967 is deficient (1 is less than 967). Euler's totient φ(967) = 966 numbers up to 967 share no factor with it.
- 4
The digits of 967 add up to 22, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 142 steps to reach 1.
967 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 968 |
| Euler totient φ(n) | 966 |
| Square | 935089 |
| Cube | 904231063 |
| Square root | 31.096624 |
| Digit sum / digital root | 22 / 4 |
| Collatz steps to 1 | 142 |
| Scientific notation | 9.67 × |
967 in other forms
| Form | Value |
|---|---|
| In words | nine hundred and sixty-seven |
| Roman numerals | CMLXVII |
| Binary (base 2) | 1111000111 |
| Octal (base 8) | 1707 |
| Hexadecimal (base 16) | 3C7 |
| Base 3 | 1022211 |
| As time | 967 seconds = 16 min 7 s |
Is 967 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 1) | 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 10) | 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 967 a prime number?
Yes. 967 is divisible only by 1 and itself.
What are the factors of 967?
1, 967.
What is 967 in binary?
1111000111 (hexadecimal 3C7, octal 1707).
What is the square root of 967?
About 31.0966.
What is 967 in Roman numerals?
CMLXVII.
Is 967 divisible by 3?
No. Its digits add up to 22, which is not a multiple of 3.
What is special about the number 967?
967 is the 163rd prime number.