The number 83988
83988 is a composite number with 18 divisors. Its prime factorisation is × × 2333. Divisors (18): 1, 2, 3, 4, 6, 9, 12, 18, 36, 2333, 4666, 6999, 9332, 13998, 20997, 27996 … 83988.
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How to work it out
- 1
What is special about 83988: a Harshad number: divisible by its digit sum 36.
- 2
83988 is composite. Its prime factorisation is
- 3
The divisors add up to 212394; without 83988 itself that is 128406, so 83988 is abundant (128406 is more than 83988). Euler's totient φ(83988) = 27984 numbers up to 83988 share no factor with it.
- 4
The digits of 83988 add up to 36, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 133 steps to reach 1.
LaTeX source of the formulas on this page
\[ 83988 = 2^{2} \times 3^{2} \times 2333 \]83988 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 18 |
| Sum of divisors | 212394 |
| Euler totient φ(n) | 27984 |
| Square | 7053984144 |
| Cube | 592450020286272 |
| Square root | 289.806832 (= 6√2333) |
| Digit sum / digital root | 36 / 9 |
| Collatz steps to 1 | 133 |
| Scientific notation | 8.3988 × |
83988 in other forms
| Form | Value |
|---|---|
| In words | eighty-three thousand nine hundred and eighty-eight |
| Binary (base 2) | 10100100000010100 |
| Octal (base 8) | 244024 |
| Hexadecimal (base 16) | 14814 |
| Base 3 | 11021012200 |
| As time | 83988 seconds = 23 h 19 min 48 s |
Is 83988 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (83988 ÷ 2 = 41994) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (83988 ÷ 3 = 27996) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (83988 ÷ 4 = 20997) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (83988 ÷ 6 = 13998) | 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 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (83988 ÷ 9 = 9332) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | 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 | Yes (83988 ÷ 12 = 6999) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 83988 a prime number?
No. 83988 = × × 2333, so it is divisible by 2.
What are the factors of 83988?
1, 2, 3, 4, 6, 9, 12, 18, 36, 2333, 4666, 6999, 9332, 13998, 20997, 27996, 41994, 83988.
What is 83988 in binary?
10100100000010100 (hexadecimal 14814, octal 244024).
What is the square root of 83988?
About 289.8068, exactly 6√2333.
Is 83988 divisible by 3?
Yes. Its digits add up to 36, a multiple of 3.
What is special about the number 83988?
83988 is a Harshad number: divisible by its digit sum 36.