The number 21624
21624 is a composite number with 32 divisors. Its prime factorisation is × 3 × 17 × 53. Divisors (32): 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 53, 68, 102, 106, 136 … 21624.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
21624 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
21624 is composite. Its prime factorisation is
- 3
The divisors add up to 58320; without 21624 itself that is 36696, so 21624 is abundant (36696 is more than 21624). Euler's totient φ(21624) = 6656 numbers up to 21624 share no factor with it.
- 4
The digits of 21624 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 162 steps to reach 1.
LaTeX source of the formulas on this page
\[ 21624 = 2^{3} \times 3 \times 17 \times 53 \]21624 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 58320 |
| Euler totient φ(n) | 6656 |
| Square | 467597376 |
| Cube | 10111325658624 |
| Square root | 147.051012 (= 2√5406) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 162 |
| Scientific notation | 2.1624 × |
21624 in other forms
| Form | Value |
|---|---|
| In words | twenty-one thousand six hundred and twenty-four |
| Binary (base 2) | 101010001111000 |
| Octal (base 8) | 52170 |
| Hexadecimal (base 16) | 5478 |
| Base 3 | 1002122220 |
| As time | 21624 seconds = 6 h 0 min 24 s |
Is 21624 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (21624 ÷ 2 = 10812) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (21624 ÷ 3 = 7208) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (21624 ÷ 4 = 5406) | 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 (21624 ÷ 6 = 3604) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 (21624 ÷ 8 = 2703) | 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 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (21624 ÷ 12 = 1802) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 21624 a prime number?
No. 21624 = × 3 × 17 × 53, so it is divisible by 2.
What are the factors of 21624?
1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 53, 68, 102, 106, 136, 159, 204, 212, 318, 408, 424, 636, 901, 1272, 1802, 2703, 3604, 5406, 7208, 10812, 21624.
What is 21624 in binary?
101010001111000 (hexadecimal 5478, octal 52170).
What is the square root of 21624?
About 147.0510, exactly 2√5406.
Is 21624 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 21624?
It is a composite number with 32 divisors.