The number 21088
21088 is a composite number with 12 divisors. Its prime factorisation is × 659. Divisors (12): 1, 2, 4, 8, 16, 32, 659, 1318, 2636, 5272, 10544, 21088.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 21088: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
21088 is composite. Its prime factorisation is
- 3
The divisors add up to 41580; without 21088 itself that is 20492, so 21088 is deficient (20492 is less than 21088). Euler's totient φ(21088) = 10528 numbers up to 21088 share no factor with it.
- 4
The digits of 21088 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 56 steps to reach 1.
LaTeX source of the formulas on this page
\[ 21088 = 2^{5} \times 659 \]21088 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 41580 |
| Euler totient φ(n) | 10528 |
| Square | 444703744 |
| Cube | 9377912553472 |
| Square root | 145.217079 (= 4√1318) |
| Digit sum / digital root | 19 / 1 |
| Collatz steps to 1 | 56 |
| Scientific notation | 2.1088 × |
21088 in other forms
| Form | Value |
|---|---|
| In words | twenty-one thousand and eighty-eight |
| Binary (base 2) | 101001001100000 |
| Octal (base 8) | 51140 |
| Hexadecimal (base 16) | 5260 |
| Base 3 | 1001221001 |
| As time | 21088 seconds = 5 h 51 min 28 s |
Is 21088 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (21088 ÷ 2 = 10544) | 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 | Yes (21088 ÷ 4 = 5272) | 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 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 | Yes (21088 ÷ 8 = 2636) | 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 | No (remainder 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 21088 a prime number?
No. 21088 = × 659, so it is divisible by 2.
What are the factors of 21088?
1, 2, 4, 8, 16, 32, 659, 1318, 2636, 5272, 10544, 21088.
What is 21088 in binary?
101001001100000 (hexadecimal 5260, octal 51140).
What is the square root of 21088?
About 145.2171, exactly 4√1318.
Is 21088 divisible by 3?
No. Its digits add up to 19, which is not a multiple of 3.
What is special about the number 21088?
21088 is a happy number: repeatedly adding the squares of its digits reaches 1.