The number 2208
2208 is a composite number with 24 divisors. Its prime factorisation is × 3 × 23. Divisors (24): 1, 2, 3, 4, 6, 8, 12, 16, 23, 24, 32, 46, 48, 69, 92, 96 … 2208.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 2208: a Harshad number: divisible by its digit sum 12.
- 2
2208 is composite. Its prime factorisation is
- 3
The divisors add up to 6048; without 2208 itself that is 3840, so 2208 is abundant (3840 is more than 2208). Euler's totient φ(2208) = 704 numbers up to 2208 share no factor with it.
- 4
The digits of 2208 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 19 steps to reach 1.
LaTeX source of the formulas on this page
\[ 2208 = 2^{5} \times 3 \times 23 \]2208 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 6048 |
| Euler totient φ(n) | 704 |
| Square | 4875264 |
| Cube | 10764582912 |
| Square root | 46.989360 (= 4√138) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 19 |
| Scientific notation | 2.208 × |
2208 in other forms
| Form | Value |
|---|---|
| In words | two thousand two hundred and eight |
| Roman numerals | MMCCVIII |
| Binary (base 2) | 100010100000 |
| Octal (base 8) | 4240 |
| Hexadecimal (base 16) | 8A0 |
| Base 3 | 10000210 |
| As time | 2208 seconds = 36 min 48 s |
Is 2208 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (2208 ÷ 2 = 1104) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (2208 ÷ 3 = 736) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (2208 ÷ 4 = 552) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (2208 ÷ 6 = 368) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 (2208 ÷ 8 = 276) | 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 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (2208 ÷ 12 = 184) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 2208 a prime number?
No. 2208 = × 3 × 23, so it is divisible by 2.
What are the factors of 2208?
1, 2, 3, 4, 6, 8, 12, 16, 23, 24, 32, 46, 48, 69, 92, 96, 138, 184, 276, 368, 552, 736, 1104, 2208.
What is 2208 in binary?
100010100000 (hexadecimal 8A0, octal 4240).
What is the square root of 2208?
About 46.9894, exactly 4√138.
What is 2208 in Roman numerals?
MMCCVIII.
Is 2208 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 2208?
2208 is a Harshad number: divisible by its digit sum 12.