The number 22400
22400 is a composite number with 48 divisors. Its prime factorisation is × × 7. Divisors (48): 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 25, 28, 32, 35, 40, 50 … 22400.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 22400: a Harshad number: divisible by its digit sum 8.
- 2
22400 is composite. Its prime factorisation is
- 3
The divisors add up to 63240; without 22400 itself that is 40840, so 22400 is abundant (40840 is more than 22400). Euler's totient φ(22400) = 7680 numbers up to 22400 share no factor with it.
- 4
The digits of 22400 add up to 8, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 87 steps to reach 1.
LaTeX source of the formulas on this page
\[ 22400 = 2^{7} \times 5^{2} \times 7 \]22400 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 63240 |
| Euler totient φ(n) | 7680 |
| Square | 501760000 |
| Cube | 11239424000000 |
| Square root | 149.666295 (= 40√14) |
| Digit sum / digital root | 8 / 8 |
| Collatz steps to 1 | 87 |
| Scientific notation | 2.24 × |
22400 in other forms
| Form | Value |
|---|---|
| In words | twenty-two thousand four hundred |
| Binary (base 2) | 101011110000000 |
| Octal (base 8) | 53600 |
| Hexadecimal (base 16) | 5780 |
| Base 3 | 1010201122 |
| As time | 22400 seconds = 6 h 13 min 20 s |
Is 22400 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (22400 ÷ 2 = 11200) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (22400 ÷ 4 = 5600) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (22400 ÷ 5 = 4480) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (22400 ÷ 7 = 3200) | 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 (22400 ÷ 8 = 2800) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 8) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (22400 ÷ 10 = 2240) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 22400 a prime number?
No. 22400 = × × 7, so it is divisible by 2.
What are the factors of 22400?
1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 25, 28, 32, 35, 40, 50, 56, 64, 70, 80, 100, 112, 128, 140, 160, 175, 200, 224, 280, 320, 350, 400, 448, 560, 640, 700, 800, 896, 1120, 1400, 1600, 2240, 2800, 3200, 4480, 5600, 11200, 22400.
What is 22400 in binary?
101011110000000 (hexadecimal 5780, octal 53600).
What is the square root of 22400?
About 149.6663, exactly 40√14.
Is 22400 divisible by 3?
No. Its digits add up to 8, which is not a multiple of 3.
What is special about the number 22400?
22400 is a Harshad number: divisible by its digit sum 8.