The number 21762
21762 is a composite number with 32 divisors. Its prime factorisation is 2 × × 13 × 31. Divisors (32): 1, 2, 3, 6, 9, 13, 18, 26, 27, 31, 39, 54, 62, 78, 93, 117 … 21762.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 21762: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
21762 is composite. Its prime factorisation is
- 3
The divisors add up to 53760; without 21762 itself that is 31998, so 21762 is abundant (31998 is more than 21762). Euler's totient φ(21762) = 6480 numbers up to 21762 share no factor with it.
- 4
The digits of 21762 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 180 steps to reach 1.
LaTeX source of the formulas on this page
\[ 21762 = 2 \times 3^{3} \times 13 \times 31 \]21762 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 53760 |
| Euler totient φ(n) | 6480 |
| Square | 473584644 |
| Cube | 10306149022728 |
| Square root | 147.519490 (= 3√2418) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 180 |
| Scientific notation | 2.1762 × |
21762 in other forms
| Form | Value |
|---|---|
| In words | twenty-one thousand seven hundred and sixty-two |
| Binary (base 2) | 101010100000010 |
| Octal (base 8) | 52402 |
| Hexadecimal (base 16) | 5502 |
| Base 3 | 1002212000 |
| As time | 21762 seconds = 6 h 2 min 42 s |
Is 21762 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (21762 ÷ 2 = 10881) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (21762 ÷ 3 = 7254) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | 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 (21762 ÷ 6 = 3627) | 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 2) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (21762 ÷ 9 = 2418) | 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 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 21762 a prime number?
No. 21762 = 2 × × 13 × 31, so it is divisible by 2.
What are the factors of 21762?
1, 2, 3, 6, 9, 13, 18, 26, 27, 31, 39, 54, 62, 78, 93, 117, 186, 234, 279, 351, 403, 558, 702, 806, 837, 1209, 1674, 2418, 3627, 7254, 10881, 21762.
What is 21762 in binary?
101010100000010 (hexadecimal 5502, octal 52402).
What is the square root of 21762?
About 147.5195, exactly 3√2418.
Is 21762 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 21762?
21762 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.