The number 21984
21984 is a composite number with 24 divisors. Its prime factorisation is × 3 × 229. Divisors (24): 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 229, 458, 687, 916 … 21984.
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How to work it out
- 1
What is special about 21984: a Harshad number: divisible by its digit sum 24.
- 2
21984 is composite. Its prime factorisation is
- 3
The divisors add up to 57960; without 21984 itself that is 35976, so 21984 is abundant (35976 is more than 21984). Euler's totient φ(21984) = 7296 numbers up to 21984 share no factor with it.
- 4
The digits of 21984 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 43 steps to reach 1.
LaTeX source of the formulas on this page
\[ 21984 = 2^{5} \times 3 \times 229 \]21984 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 57960 |
| Euler totient φ(n) | 7296 |
| Square | 483296256 |
| Cube | 10624784891904 |
| Square root | 148.270024 (= 4√1374) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 43 |
| Scientific notation | 2.1984 × |
21984 in other forms
| Form | Value |
|---|---|
| In words | twenty-one thousand nine hundred and eighty-four |
| Binary (base 2) | 101010111100000 |
| Octal (base 8) | 52740 |
| Hexadecimal (base 16) | 55E0 |
| Base 3 | 1010011020 |
| As time | 21984 seconds = 6 h 6 min 24 s |
Is 21984 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (21984 ÷ 2 = 10992) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (21984 ÷ 3 = 7328) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (21984 ÷ 4 = 5496) | 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 (21984 ÷ 6 = 3664) | 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 (21984 ÷ 8 = 2748) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | 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 | No (remainder 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (21984 ÷ 12 = 1832) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 21984 a prime number?
No. 21984 = × 3 × 229, so it is divisible by 2.
What are the factors of 21984?
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 229, 458, 687, 916, 1374, 1832, 2748, 3664, 5496, 7328, 10992, 21984.
What is 21984 in binary?
101010111100000 (hexadecimal 55E0, octal 52740).
What is the square root of 21984?
About 148.2700, exactly 4√1374.
Is 21984 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 21984?
21984 is a Harshad number: divisible by its digit sum 24.