The number 7967
7967 is a binary palindrome (1111100011111). Its prime factorisation is 31 × 257. Divisors (4): 1, 31, 257, 7967.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 7967: a binary palindrome (1111100011111); a semiprime: 31 × 257, the product of two primes.
- 2
7967 is composite. Its prime factorisation is
- 3
The divisors add up to 8256; without 7967 itself that is 289, so 7967 is deficient (289 is less than 7967). Euler's totient φ(7967) = 7680 numbers up to 7967 share no factor with it.
- 4
The digits of 7967 add up to 29, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 96 steps to reach 1.
LaTeX source of the formulas on this page
\[ 7967 = 31 \times 257 \]
7967 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 4 |
| Sum of divisors | 8256 |
| Euler totient φ(n) | 7680 |
| Square | 63473089 |
| Cube | 505690100063 |
| Square root | 89.258053 |
| Digit sum / digital root | 29 / 2 |
| Collatz steps to 1 | 96 |
| Scientific notation | 7.967 × |
7967 in other forms
| Form | Value |
|---|---|
| In words | seven thousand nine hundred and sixty-seven |
| Binary (base 2) | 1111100011111 |
| Octal (base 8) | 17437 |
| Hexadecimal (base 16) | 1F1F |
| Base 3 | 101221002 |
| As time | 7967 seconds = 2 h 12 min 47 s |
Is 7967 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 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 5) | 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 2) | 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 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 11) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 7967 a prime number?
No. 7967 = 31 × 257, so it is divisible by 31.
What are the factors of 7967?
1, 31, 257, 7967.
What is 7967 in binary?
1111100011111 (hexadecimal 1F1F, octal 17437).
What is the square root of 7967?
About 89.2581.
Is 7967 divisible by 3?
No. Its digits add up to 29, which is not a multiple of 3.
What is special about the number 7967?
7967 is a binary palindrome (1111100011111); a semiprime: 31 × 257, the product of two primes.