The number 21900
21900 is a composite number with 36 divisors. Its prime factorisation is × 3 × × 73. Divisors (36): 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 73, 75 … 21900.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 21900: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 12.
- 2
21900 is composite. Its prime factorisation is
- 3
The divisors add up to 64232; without 21900 itself that is 42332, so 21900 is abundant (42332 is more than 21900). Euler's totient φ(21900) = 5760 numbers up to 21900 share no factor with it.
- 4
The digits of 21900 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 43 steps to reach 1.
LaTeX source of the formulas on this page
\[ 21900 = 2^{2} \times 3 \times 5^{2} \times 73 \]21900 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 64232 |
| Euler totient φ(n) | 5760 |
| Square | 479610000 |
| Cube | 10503459000000 |
| Square root | 147.986486 (= 10√219) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 43 |
| Scientific notation | 2.19 × |
21900 in other forms
| Form | Value |
|---|---|
| In words | twenty-one thousand nine hundred |
| Binary (base 2) | 101010110001100 |
| Octal (base 8) | 52614 |
| Hexadecimal (base 16) | 558C |
| Base 3 | 1010001010 |
| As time | 21900 seconds = 6 h 5 min 0 s |
Is 21900 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (21900 ÷ 2 = 10950) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (21900 ÷ 3 = 7300) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (21900 ÷ 4 = 5475) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (21900 ÷ 5 = 4380) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (21900 ÷ 6 = 3650) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (21900 ÷ 10 = 2190) | 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 | Yes (21900 ÷ 12 = 1825) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 21900 a prime number?
No. 21900 = × 3 × × 73, so it is divisible by 2.
What are the factors of 21900?
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 73, 75, 100, 146, 150, 219, 292, 300, 365, 438, 730, 876, 1095, 1460, 1825, 2190, 3650, 4380, 5475, 7300, 10950, 21900.
What is 21900 in binary?
101010110001100 (hexadecimal 558C, octal 52614).
What is the square root of 21900?
About 147.9865, exactly 10√219.
Is 21900 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 21900?
21900 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 12.