The number 7820
7820 is a composite number with 24 divisors. Its prime factorisation is × 5 × 17 × 23. Divisors (24): 1, 2, 4, 5, 10, 17, 20, 23, 34, 46, 68, 85, 92, 115, 170, 230 … 7820.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 7820: a Harshad number: divisible by its digit sum 17.
- 2
7820 is composite. Its prime factorisation is
- 3
The divisors add up to 18144; without 7820 itself that is 10324, so 7820 is abundant (10324 is more than 7820). Euler's totient φ(7820) = 2816 numbers up to 7820 share no factor with it.
- 4
The digits of 7820 add up to 17, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 101 steps to reach 1.
LaTeX source of the formulas on this page
\[ 7820 = 2^{2} \times 5 \times 17 \times 23 \]7820 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 18144 |
| Euler totient φ(n) | 2816 |
| Square | 61152400 |
| Cube | 478211768000 |
| Square root | 88.430764 (= 2√1955) |
| Digit sum / digital root | 17 / 8 |
| Collatz steps to 1 | 101 |
| Scientific notation | 7.82 × |
7820 in other forms
| Form | Value |
|---|---|
| In words | seven thousand eight hundred and twenty |
| Binary (base 2) | 1111010001100 |
| Octal (base 8) | 17214 |
| Hexadecimal (base 16) | 1E8C |
| Base 3 | 101201122 |
| As time | 7820 seconds = 2 h 10 min 20 s |
Is 7820 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (7820 ÷ 2 = 3910) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (7820 ÷ 4 = 1955) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (7820 ÷ 5 = 1564) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 8) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (7820 ÷ 10 = 782) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 7820 a prime number?
No. 7820 = × 5 × 17 × 23, so it is divisible by 2.
What are the factors of 7820?
1, 2, 4, 5, 10, 17, 20, 23, 34, 46, 68, 85, 92, 115, 170, 230, 340, 391, 460, 782, 1564, 1955, 3910, 7820.
What is 7820 in binary?
1111010001100 (hexadecimal 1E8C, octal 17214).
What is the square root of 7820?
About 88.4308, exactly 2√1955.
Is 7820 divisible by 3?
No. Its digits add up to 17, which is not a multiple of 3.
What is special about the number 7820?
7820 is a Harshad number: divisible by its digit sum 17.