The number 83967
83967 is a composite number with 8 divisors. Its prime factorisation is 3 × 13 × 2153. Divisors (8): 1, 3, 13, 39, 2153, 6459, 27989, 83967.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 83967: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
83967 is composite. Its prime factorisation is
- 3
The divisors add up to 120624; without 83967 itself that is 36657, so 83967 is deficient (36657 is less than 83967). Euler's totient φ(83967) = 51648 numbers up to 83967 share no factor with it.
- 4
The digits of 83967 add up to 33, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 133 steps to reach 1.
LaTeX source of the formulas on this page
\[ 83967 = 3 \times 13 \times 2153 \]
83967 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 120624 |
| Euler totient φ(n) | 51648 |
| Square | 7050457089 |
| Cube | 592005730392063 |
| Square root | 289.770599 |
| Digit sum / digital root | 33 / 6 |
| Collatz steps to 1 | 133 |
| Scientific notation | 8.3967 × |
83967 in other forms
| Form | Value |
|---|---|
| In words | eighty-three thousand nine hundred and sixty-seven |
| Binary (base 2) | 10100011111111111 |
| Octal (base 8) | 243777 |
| Hexadecimal (base 16) | 147FF |
| Base 3 | 11021011220 |
| As time | 83967 seconds = 23 h 19 min 27 s |
Is 83967 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 | Yes (83967 ÷ 3 = 27989) | 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 3) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 6) | 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 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 3) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 83967 a prime number?
No. 83967 = 3 × 13 × 2153, so it is divisible by 3.
What are the factors of 83967?
1, 3, 13, 39, 2153, 6459, 27989, 83967.
What is 83967 in binary?
10100011111111111 (hexadecimal 147FF, octal 243777).
What is the square root of 83967?
About 289.7706.
Is 83967 divisible by 3?
Yes. Its digits add up to 33, a multiple of 3.
What is special about the number 83967?
83967 is a happy number: repeatedly adding the squares of its digits reaches 1.