The number 83188
83188 is a composite number with 12 divisors. Its prime factorisation is × 7 × 2971. Divisors (12): 1, 2, 4, 7, 14, 28, 2971, 5942, 11884, 20797, 41594, 83188.
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How to work it out
- 1
What is special about 83188: a Harshad number: divisible by its digit sum 28.
- 2
83188 is composite. Its prime factorisation is
- 3
The divisors add up to 166432; without 83188 itself that is 83244, so 83188 is abundant (83244 is more than 83188). Euler's totient φ(83188) = 35640 numbers up to 83188 share no factor with it.
- 4
The digits of 83188 add up to 28, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 151 steps to reach 1.
LaTeX source of the formulas on this page
\[ 83188 = 2^{2} \times 7 \times 2971 \]83188 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 166432 |
| Euler totient φ(n) | 35640 |
| Square | 6920243344 |
| Cube | 575681203300672 |
| Square root | 288.423300 (= 2√20797) |
| Digit sum / digital root | 28 / 1 |
| Collatz steps to 1 | 151 |
| Scientific notation | 8.3188 × |
83188 in other forms
| Form | Value |
|---|---|
| In words | eighty-three thousand one hundred and eighty-eight |
| Binary (base 2) | 10100010011110100 |
| Octal (base 8) | 242364 |
| Hexadecimal (base 16) | 144F4 |
| Base 3 | 11020010001 |
| As time | 83188 seconds = 23 h 6 min 28 s |
Is 83188 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (83188 ÷ 2 = 41594) | 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 | Yes (83188 ÷ 4 = 20797) | 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 | No (remainder 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (83188 ÷ 7 = 11884) | 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 | No (remainder 1) | 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 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 83188 a prime number?
No. 83188 = × 7 × 2971, so it is divisible by 2.
What are the factors of 83188?
1, 2, 4, 7, 14, 28, 2971, 5942, 11884, 20797, 41594, 83188.
What is 83188 in binary?
10100010011110100 (hexadecimal 144F4, octal 242364).
What is the square root of 83188?
About 288.4233, exactly 2√20797.
Is 83188 divisible by 3?
No. Its digits add up to 28, which is not a multiple of 3.
What is special about the number 83188?
83188 is a Harshad number: divisible by its digit sum 28.