The number 21801
21801 is a composite number with 12 divisors. Its prime factorisation is 3 × × 43. Divisors (12): 1, 3, 13, 39, 43, 129, 169, 507, 559, 1677, 7267, 21801.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 21801: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
21801 is composite. Its prime factorisation is
- 3
The divisors add up to 32208; without 21801 itself that is 10407, so 21801 is deficient (10407 is less than 21801). Euler's totient φ(21801) = 13104 numbers up to 21801 share no factor with it.
- 4
The digits of 21801 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 149 steps to reach 1.
LaTeX source of the formulas on this page
\[ 21801 = 3 \times 13^{2} \times 43 \]21801 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 32208 |
| Euler totient φ(n) | 13104 |
| Square | 475283601 |
| Cube | 10361657785401 |
| Square root | 147.651617 (= 13√129) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 149 |
| Scientific notation | 2.1801 × |
21801 in other forms
| Form | Value |
|---|---|
| In words | twenty-one thousand eight hundred and one |
| Binary (base 2) | 101010100101001 |
| Octal (base 8) | 52451 |
| Hexadecimal (base 16) | 5529 |
| Base 3 | 1002220110 |
| As time | 21801 seconds = 6 h 3 min 21 s |
Is 21801 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (21801 ÷ 3 = 7267) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 1) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 3) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 1) | 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 1) | 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 9) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 21801 a prime number?
No. 21801 = 3 × × 43, so it is divisible by 3.
What are the factors of 21801?
1, 3, 13, 39, 43, 129, 169, 507, 559, 1677, 7267, 21801.
What is 21801 in binary?
101010100101001 (hexadecimal 5529, octal 52451).
What is the square root of 21801?
About 147.6516, exactly 13√129.
Is 21801 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 21801?
21801 is a happy number: repeatedly adding the squares of its digits reaches 1.