The number 21924
21924 is a composite number with 48 divisors. Its prime factorisation is × × 7 × 29. Divisors (48): 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 27, 28, 29, 36, 42 … 21924.
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How to work it out
- 1
What is special about 21924: a Harshad number: divisible by its digit sum 18.
- 2
21924 is composite. Its prime factorisation is
- 3
The divisors add up to 67200; without 21924 itself that is 45276, so 21924 is abundant (45276 is more than 21924). Euler's totient φ(21924) = 6048 numbers up to 21924 share no factor with it.
- 4
The digits of 21924 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 43 steps to reach 1.
LaTeX source of the formulas on this page
\[ 21924 = 2^{2} \times 3^{3} \times 7 \times 29 \]21924 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 67200 |
| Euler totient φ(n) | 6048 |
| Square | 480661776 |
| Cube | 10538028777024 |
| Square root | 148.067552 (= 6√609) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 43 |
| Scientific notation | 2.1924 × |
21924 in other forms
| Form | Value |
|---|---|
| In words | twenty-one thousand nine hundred and twenty-four |
| Binary (base 2) | 101010110100100 |
| Octal (base 8) | 52644 |
| Hexadecimal (base 16) | 55A4 |
| Base 3 | 1010002000 |
| As time | 21924 seconds = 6 h 5 min 24 s |
Is 21924 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (21924 ÷ 2 = 10962) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (21924 ÷ 3 = 7308) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (21924 ÷ 4 = 5481) | 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 (21924 ÷ 6 = 3654) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (21924 ÷ 7 = 3132) | 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 | Yes (21924 ÷ 9 = 2436) | 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 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (21924 ÷ 12 = 1827) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 21924 a prime number?
No. 21924 = × × 7 × 29, so it is divisible by 2.
What are the factors of 21924?
1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 27, 28, 29, 36, 42, 54, 58, 63, 84, 87, 108, 116, 126, 174, 189, 203, 252, 261, 348, 378, 406, 522, 609, 756, 783, 812, 1044, 1218, 1566, 1827, 2436, 3132, 3654, 5481, 7308, 10962, 21924.
What is 21924 in binary?
101010110100100 (hexadecimal 55A4, octal 52644).
What is the square root of 21924?
About 148.0676, exactly 6√609.
Is 21924 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 21924?
21924 is a Harshad number: divisible by its digit sum 18.