The number 21792
21792 is a composite number with 24 divisors. Its prime factorisation is × 3 × 227. Divisors (24): 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 227, 454, 681, 908 … 21792.
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How to work it out
- 1
What is special about 21792: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
21792 is composite. Its prime factorisation is
- 3
The divisors add up to 57456; without 21792 itself that is 35664, so 21792 is abundant (35664 is more than 21792). Euler's totient φ(21792) = 7232 numbers up to 21792 share no factor with it.
- 4
The digits of 21792 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 69 steps to reach 1.
LaTeX source of the formulas on this page
\[ 21792 = 2^{5} \times 3 \times 227 \]21792 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 57456 |
| Euler totient φ(n) | 7232 |
| Square | 474891264 |
| Cube | 10348830425088 |
| Square root | 147.621137 (= 4√1362) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 69 |
| Scientific notation | 2.1792 × |
21792 in other forms
| Form | Value |
|---|---|
| In words | twenty-one thousand seven hundred and ninety-two |
| Binary (base 2) | 101010100100000 |
| Octal (base 8) | 52440 |
| Hexadecimal (base 16) | 5520 |
| Base 3 | 1002220010 |
| As time | 21792 seconds = 6 h 3 min 12 s |
Is 21792 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (21792 ÷ 2 = 10896) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (21792 ÷ 3 = 7264) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (21792 ÷ 4 = 5448) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (21792 ÷ 6 = 3632) | 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 | Yes (21792 ÷ 8 = 2724) | 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 2) | 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 (21792 ÷ 12 = 1816) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 21792 a prime number?
No. 21792 = × 3 × 227, so it is divisible by 2.
What are the factors of 21792?
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 227, 454, 681, 908, 1362, 1816, 2724, 3632, 5448, 7264, 10896, 21792.
What is 21792 in binary?
101010100100000 (hexadecimal 5520, octal 52440).
What is the square root of 21792?
About 147.6211, exactly 4√1362.
Is 21792 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 21792?
21792 is a happy number: repeatedly adding the squares of its digits reaches 1.