The number 8220
8220 is a composite number with 24 divisors. Its prime factorisation is × 3 × 5 × 137. Divisors (24): 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 137, 274, 411, 548 … 8220.
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How to work it out
- 1
What is special about 8220: a Harshad number: divisible by its digit sum 12.
- 2
8220 is composite. Its prime factorisation is
- 3
The divisors add up to 23184; without 8220 itself that is 14964, so 8220 is abundant (14964 is more than 8220). Euler's totient φ(8220) = 2176 numbers up to 8220 share no factor with it.
- 4
The digits of 8220 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 39 steps to reach 1.
LaTeX source of the formulas on this page
\[ 8220 = 2^{2} \times 3 \times 5 \times 137 \]8220 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 23184 |
| Euler totient φ(n) | 2176 |
| Square | 67568400 |
| Cube | 555412248000 |
| Square root | 90.664216 (= 2√2055) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 39 |
| Scientific notation | 8.22 × |
8220 in other forms
| Form | Value |
|---|---|
| In words | eight thousand two hundred and twenty |
| Binary (base 2) | 10000000011100 |
| Octal (base 8) | 20034 |
| Hexadecimal (base 16) | 201C |
| Base 3 | 102021110 |
| As time | 8220 seconds = 2 h 17 min 0 s |
Is 8220 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (8220 ÷ 2 = 4110) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (8220 ÷ 3 = 2740) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (8220 ÷ 4 = 2055) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (8220 ÷ 5 = 1644) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (8220 ÷ 6 = 1370) | 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 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (8220 ÷ 10 = 822) | 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 (8220 ÷ 12 = 685) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 8220 a prime number?
No. 8220 = × 3 × 5 × 137, so it is divisible by 2.
What are the factors of 8220?
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 137, 274, 411, 548, 685, 822, 1370, 1644, 2055, 2740, 4110, 8220.
What is 8220 in binary?
10000000011100 (hexadecimal 201C, octal 20034).
What is the square root of 8220?
About 90.6642, exactly 2√2055.
Is 8220 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 8220?
8220 is a Harshad number: divisible by its digit sum 12.