The number 208
208 is a composite number with 10 divisors. Its prime factorisation is × 13. Divisors (10): 1, 2, 4, 8, 13, 16, 26, 52, 104, 208.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 208: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
208 is composite. Its prime factorisation is
- 3
The divisors add up to 434; without 208 itself that is 226, so 208 is abundant (226 is more than 208). Euler's totient φ(208) = 96 numbers up to 208 share no factor with it.
- 4
The digits of 208 add up to 10, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 13 steps to reach 1.
LaTeX source of the formulas on this page
\[ 208 = 2^{4} \times 13 \]208 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 10 |
| Sum of divisors | 434 |
| Euler totient φ(n) | 96 |
| Square | 43264 |
| Cube | 8998912 |
| Square root | 14.422205 (= 4√13) |
| Digit sum / digital root | 10 / 1 |
| Collatz steps to 1 | 13 |
| Scientific notation | 2.08 × |
208 in other forms
| Form | Value |
|---|---|
| In words | two hundred and eight |
| Roman numerals | CCVIII |
| Binary (base 2) | 11010000 |
| Octal (base 8) | 320 |
| Hexadecimal (base 16) | D0 |
| Base 3 | 21201 |
| As time | 208 seconds = 3 min 28 s |
Is 208 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (208 ÷ 2 = 104) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (208 ÷ 4 = 52) | 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 | No (remainder 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (208 ÷ 8 = 26) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 1) | 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 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 208 a prime number?
No. 208 = × 13, so it is divisible by 2.
What are the factors of 208?
1, 2, 4, 8, 13, 16, 26, 52, 104, 208.
What is 208 in binary?
11010000 (hexadecimal D0, octal 320).
What is the square root of 208?
About 14.4222, exactly 4√13.
What is 208 in Roman numerals?
CCVIII.
Is 208 divisible by 3?
No. Its digits add up to 10, which is not a multiple of 3.
What is special about the number 208?
208 is a happy number: repeatedly adding the squares of its digits reaches 1.