The number 8397
8397 is a composite number with 8 divisors. Its prime factorisation is × 311. Divisors (8): 1, 3, 9, 27, 311, 933, 2799, 8397.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 8397: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 27.
- 2
8397 is composite. Its prime factorisation is
- 3
The divisors add up to 12480; without 8397 itself that is 4083, so 8397 is deficient (4083 is less than 8397). Euler's totient φ(8397) = 5580 numbers up to 8397 share no factor with it.
- 4
The digits of 8397 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 65 steps to reach 1.
LaTeX source of the formulas on this page
\[ 8397 = 3^{3} \times 311 \]8397 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 12480 |
| Euler totient φ(n) | 5580 |
| Square | 70509609 |
| Cube | 592069186773 |
| Square root | 91.635146 (= 3√933) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 65 |
| Scientific notation | 8.397 × |
8397 in other forms
| Form | Value |
|---|---|
| In words | eight thousand three hundred and ninety-seven |
| Binary (base 2) | 10000011001101 |
| Octal (base 8) | 20315 |
| Hexadecimal (base 16) | 20CD |
| Base 3 | 102112000 |
| As time | 8397 seconds = 2 h 19 min 57 s |
Is 8397 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 (8397 ÷ 3 = 2799) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 1) | 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 4) | 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 5) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (8397 ÷ 9 = 933) | 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 9) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 8397 a prime number?
No. 8397 = × 311, so it is divisible by 3.
What are the factors of 8397?
1, 3, 9, 27, 311, 933, 2799, 8397.
What is 8397 in binary?
10000011001101 (hexadecimal 20CD, octal 20315).
What is the square root of 8397?
About 91.6351, exactly 3√933.
Is 8397 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 8397?
8397 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 27.