The number 21105
21105 is a composite number with 24 divisors. Its prime factorisation is × 5 × 7 × 67. Divisors (24): 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 67, 105, 201, 315, 335, 469 … 21105.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 21105: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.
- 2
21105 is composite. Its prime factorisation is
- 3
The divisors add up to 42432; without 21105 itself that is 21327, so 21105 is abundant (21327 is more than 21105). Euler's totient φ(21105) = 9504 numbers up to 21105 share no factor with it.
- 4
The digits of 21105 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
\[ 21105 = 3^{2} \times 5 \times 7 \times 67 \]21105 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 42432 |
| Euler totient φ(n) | 9504 |
| Square | 445421025 |
| Cube | 9400610732625 |
| Square root | 145.275600 (= 3√2345) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 56 |
| Scientific notation | 2.1105 × |
21105 in other forms
| Form | Value |
|---|---|
| In words | twenty-one thousand one hundred and five |
| Binary (base 2) | 101001001110001 |
| Octal (base 8) | 51161 |
| Hexadecimal (base 16) | 5271 |
| Base 3 | 1001221200 |
| As time | 21105 seconds = 5 h 51 min 45 s |
Is 21105 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 (21105 ÷ 3 = 7035) | 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 | Yes (21105 ÷ 5 = 4221) | 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 | Yes (21105 ÷ 7 = 3015) | 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 (21105 ÷ 9 = 2345) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 5) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | 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 21105 a prime number?
No. 21105 = × 5 × 7 × 67, so it is divisible by 3.
What are the factors of 21105?
1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 67, 105, 201, 315, 335, 469, 603, 1005, 1407, 2345, 3015, 4221, 7035, 21105.
What is 21105 in binary?
101001001110001 (hexadecimal 5271, octal 51161).
What is the square root of 21105?
About 145.2756, exactly 3√2345.
Is 21105 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 21105?
21105 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.