The number 7824
7824 is a composite number with 20 divisors. Its prime factorisation is × 3 × 163. Divisors (20): 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 163, 326, 489, 652, 978, 1304 … 7824.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 7824: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
7824 is composite. Its prime factorisation is
- 3
The divisors add up to 20336; without 7824 itself that is 12512, so 7824 is abundant (12512 is more than 7824). Euler's totient φ(7824) = 2592 numbers up to 7824 share no factor with it.
- 4
The digits of 7824 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 52 steps to reach 1.
LaTeX source of the formulas on this page
\[ 7824 = 2^{4} \times 3 \times 163 \]7824 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 20336 |
| Euler totient φ(n) | 2592 |
| Square | 61214976 |
| Cube | 478945972224 |
| Square root | 88.453378 (= 4√489) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 52 |
| Scientific notation | 7.824 × |
7824 in other forms
| Form | Value |
|---|---|
| In words | seven thousand eight hundred and twenty-four |
| Binary (base 2) | 1111010010000 |
| Octal (base 8) | 17220 |
| Hexadecimal (base 16) | 1E90 |
| Base 3 | 101201210 |
| As time | 7824 seconds = 2 h 10 min 24 s |
Is 7824 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (7824 ÷ 2 = 3912) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (7824 ÷ 3 = 2608) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (7824 ÷ 4 = 1956) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (7824 ÷ 6 = 1304) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (7824 ÷ 8 = 978) | 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 4) | 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 (7824 ÷ 12 = 652) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 7824 a prime number?
No. 7824 = × 3 × 163, so it is divisible by 2.
What are the factors of 7824?
1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 163, 326, 489, 652, 978, 1304, 1956, 2608, 3912, 7824.
What is 7824 in binary?
1111010010000 (hexadecimal 1E90, octal 17220).
What is the square root of 7824?
About 88.4534, exactly 4√489.
Is 7824 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 7824?
7824 is a happy number: repeatedly adding the squares of its digits reaches 1.