The number 21384
21384 is a composite number with 48 divisors. Its prime factorisation is × × 11. Divisors (48): 1, 2, 3, 4, 6, 8, 9, 11, 12, 18, 22, 24, 27, 33, 36, 44 … 21384.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 21384: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
21384 is composite. Its prime factorisation is
- 3
The divisors add up to 65520; without 21384 itself that is 44136, so 21384 is abundant (44136 is more than 21384). Euler's totient φ(21384) = 6480 numbers up to 21384 share no factor with it.
- 4
The digits of 21384 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 118 steps to reach 1.
LaTeX source of the formulas on this page
\[ 21384 = 2^{3} \times 3^{5} \times 11 \]21384 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 65520 |
| Euler totient φ(n) | 6480 |
| Square | 457275456 |
| Cube | 9778378351104 |
| Square root | 146.232691 (= 18√66) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 118 |
| Scientific notation | 2.1384 × |
21384 in other forms
| Form | Value |
|---|---|
| In words | twenty-one thousand three hundred and eighty-four |
| Binary (base 2) | 101001110001000 |
| Octal (base 8) | 51610 |
| Hexadecimal (base 16) | 5388 |
| Base 3 | 1002100000 |
| As time | 21384 seconds = 5 h 56 min 24 s |
Is 21384 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (21384 ÷ 2 = 10692) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (21384 ÷ 3 = 7128) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (21384 ÷ 4 = 5346) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (21384 ÷ 6 = 3564) | 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 (21384 ÷ 8 = 2673) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (21384 ÷ 9 = 2376) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (21384 ÷ 11 = 1944) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (21384 ÷ 12 = 1782) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 21384 a prime number?
No. 21384 = × × 11, so it is divisible by 2.
What are the factors of 21384?
1, 2, 3, 4, 6, 8, 9, 11, 12, 18, 22, 24, 27, 33, 36, 44, 54, 66, 72, 81, 88, 99, 108, 132, 162, 198, 216, 243, 264, 297, 324, 396, 486, 594, 648, 792, 891, 972, 1188, 1782, 1944, 2376, 2673, 3564, 5346, 7128, 10692, 21384.
What is 21384 in binary?
101001110001000 (hexadecimal 5388, octal 51610).
What is the square root of 21384?
About 146.2327, exactly 18√66.
Is 21384 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 21384?
21384 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.