The number 82008
82008 is a composite number with 48 divisors. Its prime factorisation is × × 17 × 67. Divisors (48): 1, 2, 3, 4, 6, 8, 9, 12, 17, 18, 24, 34, 36, 51, 67, 68 … 82008.
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How to work it out
- 1
What is special about 82008: a Harshad number: divisible by its digit sum 18.
- 2
82008 is composite. Its prime factorisation is
- 3
The divisors add up to 238680; without 82008 itself that is 156672, so 82008 is abundant (156672 is more than 82008). Euler's totient φ(82008) = 25344 numbers up to 82008 share no factor with it.
- 4
The digits of 82008 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 151 steps to reach 1.
LaTeX source of the formulas on this page
\[ 82008 = 2^{3} \times 3^{2} \times 17 \times 67 \]82008 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 238680 |
| Euler totient φ(n) | 25344 |
| Square | 6725312064 |
| Cube | 551529391744512 |
| Square root | 286.370390 (= 6√2278) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 151 |
| Scientific notation | 8.2008 × |
82008 in other forms
| Form | Value |
|---|---|
| In words | eighty-two thousand and eight |
| Binary (base 2) | 10100000001011000 |
| Octal (base 8) | 240130 |
| Hexadecimal (base 16) | 14058 |
| Base 3 | 11011111100 |
| As time | 82008 seconds = 22 h 46 min 48 s |
Is 82008 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (82008 ÷ 2 = 41004) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (82008 ÷ 3 = 27336) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (82008 ÷ 4 = 20502) | 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 (82008 ÷ 6 = 13668) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 | Yes (82008 ÷ 8 = 10251) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (82008 ÷ 9 = 9112) | 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 (82008 ÷ 12 = 6834) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 82008 a prime number?
No. 82008 = × × 17 × 67, so it is divisible by 2.
What are the factors of 82008?
1, 2, 3, 4, 6, 8, 9, 12, 17, 18, 24, 34, 36, 51, 67, 68, 72, 102, 134, 136, 153, 201, 204, 268, 306, 402, 408, 536, 603, 612, 804, 1139, 1206, 1224, 1608, 2278, 2412, 3417, 4556, 4824, 6834, 9112, 10251, 13668, 20502, 27336, 41004, 82008.
What is 82008 in binary?
10100000001011000 (hexadecimal 14058, octal 240130).
What is the square root of 82008?
About 286.3704, exactly 6√2278.
Is 82008 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 82008?
82008 is a Harshad number: divisible by its digit sum 18.