The number 19824
19824 is a composite number with 40 divisors. Its prime factorisation is × 3 × 7 × 59. Divisors (40): 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56 … 19824.
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How to work it out
- 1
What is special about 19824: a Harshad number: divisible by its digit sum 24.
- 2
19824 is composite. Its prime factorisation is
- 3
The divisors add up to 59520; without 19824 itself that is 39696, so 19824 is abundant (39696 is more than 19824). Euler's totient φ(19824) = 5568 numbers up to 19824 share no factor with it.
- 4
The digits of 19824 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 136 steps to reach 1.
LaTeX source of the formulas on this page
\[ 19824 = 2^{4} \times 3 \times 7 \times 59 \]19824 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 59520 |
| Euler totient φ(n) | 5568 |
| Square | 392990976 |
| Cube | 7790653108224 |
| Square root | 140.797727 (= 4√1239) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 136 |
| Scientific notation | 1.9824 × |
19824 in other forms
| Form | Value |
|---|---|
| In words | nineteen thousand eight hundred and twenty-four |
| Binary (base 2) | 100110101110000 |
| Octal (base 8) | 46560 |
| Hexadecimal (base 16) | 4D70 |
| Base 3 | 1000012020 |
| As time | 19824 seconds = 5 h 30 min 24 s |
Is 19824 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (19824 ÷ 2 = 9912) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (19824 ÷ 3 = 6608) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (19824 ÷ 4 = 4956) | 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 (19824 ÷ 6 = 3304) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (19824 ÷ 7 = 2832) | 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 (19824 ÷ 8 = 2478) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | 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 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (19824 ÷ 12 = 1652) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 19824 a prime number?
No. 19824 = × 3 × 7 × 59, so it is divisible by 2.
What are the factors of 19824?
1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 59, 84, 112, 118, 168, 177, 236, 336, 354, 413, 472, 708, 826, 944, 1239, 1416, 1652, 2478, 2832, 3304, 4956, 6608, 9912, 19824.
What is 19824 in binary?
100110101110000 (hexadecimal 4D70, octal 46560).
What is the square root of 19824?
About 140.7977, exactly 4√1239.
Is 19824 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 19824?
19824 is a Harshad number: divisible by its digit sum 24.