The number 21504
21504 is a composite number with 44 divisors. Its prime factorisation is × 3 × 7. Divisors (44): 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48 … 21504.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 21504: a Harshad number: divisible by its digit sum 12.
- 2
21504 is composite. Its prime factorisation is
- 3
The divisors add up to 65504; without 21504 itself that is 44000, so 21504 is abundant (44000 is more than 21504). Euler's totient φ(21504) = 6144 numbers up to 21504 share no factor with it.
- 4
The digits of 21504 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 17 steps to reach 1.
LaTeX source of the formulas on this page
\[ 21504 = 2^{10} \times 3 \times 7 \]21504 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 44 |
| Sum of divisors | 65504 |
| Euler totient φ(n) | 6144 |
| Square | 462422016 |
| Cube | 9943923032064 |
| Square root | 146.642422 (= 32√21) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 17 |
| Scientific notation | 2.1504 × |
21504 in other forms
| Form | Value |
|---|---|
| In words | twenty-one thousand five hundred and four |
| Binary (base 2) | 101010000000000 |
| Octal (base 8) | 52000 |
| Hexadecimal (base 16) | 5400 |
| Base 3 | 1002111110 |
| As time | 21504 seconds = 5 h 58 min 24 s |
Is 21504 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (21504 ÷ 2 = 10752) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (21504 ÷ 3 = 7168) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (21504 ÷ 4 = 5376) | 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 (21504 ÷ 6 = 3584) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (21504 ÷ 7 = 3072) | 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 (21504 ÷ 8 = 2688) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | 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 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (21504 ÷ 12 = 1792) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 21504 a prime number?
No. 21504 = × 3 × 7, so it is divisible by 2.
What are the factors of 21504?
1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 64, 84, 96, 112, 128, 168, 192, 224, 256, 336, 384, 448, 512, 672, 768, 896, 1024, 1344, 1536, 1792, 2688, 3072, 3584, 5376, 7168, 10752, 21504.
What is 21504 in binary?
101010000000000 (hexadecimal 5400, octal 52000).
What is the square root of 21504?
About 146.6424, exactly 32√21.
Is 21504 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 21504?
21504 is a Harshad number: divisible by its digit sum 12.