The number 85008
85008 is a composite number with 80 divisors. Its prime factorisation is × 3 × 7 × 11 × 23. Divisors (80): 1, 2, 3, 4, 6, 7, 8, 11, 12, 14, 16, 21, 22, 23, 24, 28 … 85008.
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How to work it out
- 1
What is special about 85008: a Harshad number: divisible by its digit sum 21.
- 2
85008 is composite. Its prime factorisation is
- 3
The divisors add up to 285696; without 85008 itself that is 200688, so 85008 is abundant (200688 is more than 85008). Euler's totient φ(85008) = 21120 numbers up to 85008 share no factor with it.
- 4
The digits of 85008 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 58 steps to reach 1.
LaTeX source of the formulas on this page
\[ 85008 = 2^{4} \times 3 \times 7 \times 11 \times 23 \]85008 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 80 |
| Sum of divisors | 285696 |
| Euler totient φ(n) | 21120 |
| Square | 7226360064 |
| Cube | 614298416320512 |
| Square root | 291.561314 (= 4√5313) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 58 |
| Scientific notation | 8.5008 × |
85008 in other forms
| Form | Value |
|---|---|
| In words | eighty-five thousand and eight |
| Binary (base 2) | 10100110000010000 |
| Octal (base 8) | 246020 |
| Hexadecimal (base 16) | 14C10 |
| Base 3 | 11022121110 |
| As time | 85008 seconds = 23 h 36 min 48 s |
Is 85008 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (85008 ÷ 2 = 42504) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (85008 ÷ 3 = 28336) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (85008 ÷ 4 = 21252) | 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 (85008 ÷ 6 = 14168) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (85008 ÷ 7 = 12144) | 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 (85008 ÷ 8 = 10626) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | 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 | Yes (85008 ÷ 11 = 7728) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (85008 ÷ 12 = 7084) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 85008 a prime number?
No. 85008 = × 3 × 7 × 11 × 23, so it is divisible by 2.
What are the factors of 85008?
1, 2, 3, 4, 6, 7, 8, 11, 12, 14, 16, 21, 22, 23, 24, 28, 33, 42, 44, 46, 48, 56, 66, 69, 77, 84, 88, 92, 112, 132, 138, 154, 161, 168, 176, 184, 231, 253, 264, 276, 308, 322, 336, 368, 462, 483, 506, 528, 552, 616, 644, 759, 924, 966, 1012, 1104, 1232, 1288, 1518, 1771, 1848, 1932, 2024, 2576, 3036, 3542, 3696, 3864, 4048, 5313, 6072, 7084, 7728, 10626, 12144, 14168, 21252, 28336, 42504, 85008.
What is 85008 in binary?
10100110000010000 (hexadecimal 14C10, octal 246020).
What is the square root of 85008?
About 291.5613, exactly 4√5313.
Is 85008 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 85008?
85008 is a Harshad number: divisible by its digit sum 21.