The number 22464
22464 is a composite number with 56 divisors. Its prime factorisation is × × 13. Divisors (56): 1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 24, 26, 27, 32, 36 … 22464.
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How to work it out
- 1
What is special about 22464: a Harshad number: divisible by its digit sum 18.
- 2
22464 is composite. Its prime factorisation is
- 3
The divisors add up to 71120; without 22464 itself that is 48656, so 22464 is abundant (48656 is more than 22464). Euler's totient φ(22464) = 6912 numbers up to 22464 share no factor with it.
- 4
The digits of 22464 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 87 steps to reach 1.
LaTeX source of the formulas on this page
\[ 22464 = 2^{6} \times 3^{3} \times 13 \]22464 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 56 |
| Sum of divisors | 71120 |
| Euler totient φ(n) | 6912 |
| Square | 504631296 |
| Cube | 11336037433344 |
| Square root | 149.879952 (= 24√39) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 87 |
| Scientific notation | 2.2464 × |
22464 in other forms
| Form | Value |
|---|---|
| In words | twenty-two thousand four hundred and sixty-four |
| Binary (base 2) | 101011111000000 |
| Octal (base 8) | 53700 |
| Hexadecimal (base 16) | 57C0 |
| Base 3 | 1010211000 |
| As time | 22464 seconds = 6 h 14 min 24 s |
Is 22464 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (22464 ÷ 2 = 11232) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (22464 ÷ 3 = 7488) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (22464 ÷ 4 = 5616) | 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 (22464 ÷ 6 = 3744) | 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 (22464 ÷ 8 = 2808) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (22464 ÷ 9 = 2496) | 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 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (22464 ÷ 12 = 1872) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 22464 a prime number?
No. 22464 = × × 13, so it is divisible by 2.
What are the factors of 22464?
1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 24, 26, 27, 32, 36, 39, 48, 52, 54, 64, 72, 78, 96, 104, 108, 117, 144, 156, 192, 208, 216, 234, 288, 312, 351, 416, 432, 468, 576, 624, 702, 832, 864, 936, 1248, 1404, 1728, 1872, 2496, 2808, 3744, 5616, 7488, 11232, 22464.
What is 22464 in binary?
101011111000000 (hexadecimal 57C0, octal 53700).
What is the square root of 22464?
About 149.8800, exactly 24√39.
Is 22464 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 22464?
22464 is a Harshad number: divisible by its digit sum 18.