The number 21321
21321 is a triangular number: 1 + 2 + … + 206 = 21321. Its prime factorisation is × 23 × 103. Divisors (12): 1, 3, 9, 23, 69, 103, 207, 309, 927, 2369, 7107, 21321.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 21321: a triangular number: 1 + 2 + … + 206 = 21321; a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.
- 2
21321 is composite. Its prime factorisation is
- 3
The divisors add up to 32448; without 21321 itself that is 11127, so 21321 is deficient (11127 is less than 21321). Euler's totient φ(21321) = 13464 numbers up to 21321 share no factor with it.
- 4
The digits of 21321 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 56 steps to reach 1.
LaTeX source of the formulas on this page
\[ 21321 = 3^{2} \times 23 \times 103 \]21321 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 32448 |
| Euler totient φ(n) | 13464 |
| Square | 454585041 |
| Cube | 9692207659161 |
| Square root | 146.017122 (= 3√2369) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 56 |
| Scientific notation | 2.1321 × |
21321 in other forms
| Form | Value |
|---|---|
| In words | twenty-one thousand three hundred and twenty-one |
| Binary (base 2) | 101001101001001 |
| Octal (base 8) | 51511 |
| Hexadecimal (base 16) | 5349 |
| Base 3 | 1002020200 |
| As time | 21321 seconds = 5 h 55 min 21 s |
Is 21321 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 (21321 ÷ 3 = 7107) | 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 6) | 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 | Yes (21321 ÷ 9 = 2369) | 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 3) | 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 21321 a prime number?
No. 21321 = × 23 × 103, so it is divisible by 3.
What are the factors of 21321?
1, 3, 9, 23, 69, 103, 207, 309, 927, 2369, 7107, 21321.
What is 21321 in binary?
101001101001001 (hexadecimal 5349, octal 51511).
What is the square root of 21321?
About 146.0171, exactly 3√2369.
Is 21321 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 21321?
21321 is a triangular number: 1 + 2 + … + 206 = 21321; a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.