The number 21538
21538 is a composite number with 12 divisors. Its prime factorisation is 2 × × 89. Divisors (12): 1, 2, 11, 22, 89, 121, 178, 242, 979, 1958, 10769, 21538.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 21538: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
21538 is composite. Its prime factorisation is
- 3
The divisors add up to 35910; without 21538 itself that is 14372, so 21538 is deficient (14372 is less than 21538). Euler's totient φ(21538) = 9680 numbers up to 21538 share no factor with it.
- 4
The digits of 21538 add up to 19, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 118 steps to reach 1.
LaTeX source of the formulas on this page
\[ 21538 = 2 \times 11^{2} \times 89 \]21538 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 35910 |
| Euler totient φ(n) | 9680 |
| Square | 463885444 |
| Cube | 9991164692872 |
| Square root | 146.758305 (= 11√178) |
| Digit sum / digital root | 19 / 1 |
| Collatz steps to 1 | 118 |
| Scientific notation | 2.1538 × |
21538 in other forms
| Form | Value |
|---|---|
| In words | twenty-one thousand five hundred and thirty-eight |
| Binary (base 2) | 101010000100010 |
| Octal (base 8) | 52042 |
| Hexadecimal (base 16) | 5422 |
| Base 3 | 1002112201 |
| As time | 21538 seconds = 5 h 58 min 58 s |
Is 21538 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (21538 ÷ 2 = 10769) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | 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 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 4) | 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 | No (remainder 1) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (21538 ÷ 11 = 1958) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 10) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 21538 a prime number?
No. 21538 = 2 × × 89, so it is divisible by 2.
What are the factors of 21538?
1, 2, 11, 22, 89, 121, 178, 242, 979, 1958, 10769, 21538.
What is 21538 in binary?
101010000100010 (hexadecimal 5422, octal 52042).
What is the square root of 21538?
About 146.7583, exactly 11√178.
Is 21538 divisible by 3?
No. Its digits add up to 19, which is not a multiple of 3.
What is special about the number 21538?
21538 is a happy number: repeatedly adding the squares of its digits reaches 1.