The number 21328
21328 is a composite number with 20 divisors. Its prime factorisation is × 31 × 43. Divisors (20): 1, 2, 4, 8, 16, 31, 43, 62, 86, 124, 172, 248, 344, 496, 688, 1333 … 21328.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 21328: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 16.
- 2
21328 is composite. Its prime factorisation is
- 3
The divisors add up to 43648; without 21328 itself that is 22320, so 21328 is abundant (22320 is more than 21328). Euler's totient φ(21328) = 10080 numbers up to 21328 share no factor with it.
- 4
The digits of 21328 add up to 16, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 118 steps to reach 1.
LaTeX source of the formulas on this page
\[ 21328 = 2^{4} \times 31 \times 43 \]21328 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 43648 |
| Euler totient φ(n) | 10080 |
| Square | 454883584 |
| Cube | 9701757079552 |
| Square root | 146.041090 (= 4√1333) |
| Digit sum / digital root | 16 / 7 |
| Collatz steps to 1 | 118 |
| Scientific notation | 2.1328 × |
21328 in other forms
| Form | Value |
|---|---|
| In words | twenty-one thousand three hundred and twenty-eight |
| Binary (base 2) | 101001101010000 |
| Octal (base 8) | 51520 |
| Hexadecimal (base 16) | 5350 |
| Base 3 | 1002020221 |
| As time | 21328 seconds = 5 h 55 min 28 s |
Is 21328 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (21328 ÷ 2 = 10664) | 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 (21328 ÷ 4 = 5332) | 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 | Yes (21328 ÷ 8 = 2666) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | 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 10) | 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 21328 a prime number?
No. 21328 = × 31 × 43, so it is divisible by 2.
What are the factors of 21328?
1, 2, 4, 8, 16, 31, 43, 62, 86, 124, 172, 248, 344, 496, 688, 1333, 2666, 5332, 10664, 21328.
What is 21328 in binary?
101001101010000 (hexadecimal 5350, octal 51520).
What is the square root of 21328?
About 146.0411, exactly 4√1333.
Is 21328 divisible by 3?
No. Its digits add up to 16, which is not a multiple of 3.
What is special about the number 21328?
21328 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 16.