The number 3967
3967 is the 549th prime number. Its only divisors are 1 and 3967.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 3967: the 549th prime number.
- 2
3967 is prime, so its only factors are 1 and 3967. It is the 549th prime; the next prime is 3989 and the one before is 3947.
- 3
The divisors add up to 3968; without 3967 itself that is 1, so 3967 is deficient (1 is less than 3967). Euler's totient φ(3967) = 3966 numbers up to 3967 share no factor with it.
- 4
The digits of 3967 add up to 25, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 51 steps to reach 1.
3967 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 3968 |
| Euler totient φ(n) | 3966 |
| Square | 15737089 |
| Cube | 62429032063 |
| Square root | 62.984125 |
| Digit sum / digital root | 25 / 7 |
| Collatz steps to 1 | 51 |
| Scientific notation | 3.967 × |
3967 in other forms
| Form | Value |
|---|---|
| In words | three thousand nine hundred and sixty-seven |
| Roman numerals | MMMCMLXVII |
| Binary (base 2) | 111101111111 |
| Octal (base 8) | 7577 |
| Hexadecimal (base 16) | F7F |
| Base 3 | 12102221 |
| As time | 3967 seconds = 1 h 6 min 7 s |
Is 3967 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 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 7) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | 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 7) | 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 3967 a prime number?
Yes. 3967 is divisible only by 1 and itself.
What are the factors of 3967?
1, 3967.
What is 3967 in binary?
111101111111 (hexadecimal F7F, octal 7577).
What is the square root of 3967?
About 62.9841.
What is 3967 in Roman numerals?
MMMCMLXVII.
Is 3967 divisible by 3?
No. Its digits add up to 25, which is not a multiple of 3.
What is special about the number 3967?
3967 is the 549th prime number.