The number 680
680 is a composite number with 16 divisors. Its prime factorisation is × 5 × 17. Divisors (16): 1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, 680.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 680: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
680 is composite. Its prime factorisation is
- 3
The divisors add up to 1620; without 680 itself that is 940, so 680 is abundant (940 is more than 680). Euler's totient φ(680) = 256 numbers up to 680 share no factor with it.
- 4
The digits of 680 add up to 14, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 12 steps to reach 1.
LaTeX source of the formulas on this page
\[ 680 = 2^{3} \times 5 \times 17 \]680 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 1620 |
| Euler totient φ(n) | 256 |
| Square | 462400 |
| Cube | 314432000 |
| Square root | 26.076810 (= 2√170) |
| Digit sum / digital root | 14 / 5 |
| Collatz steps to 1 | 12 |
| Scientific notation | 6.8 × |
680 in other forms
| Form | Value |
|---|---|
| In words | six hundred and eighty |
| Roman numerals | DCLXXX |
| Binary (base 2) | 1010101000 |
| Octal (base 8) | 1250 |
| Hexadecimal (base 16) | 2A8 |
| Base 3 | 221012 |
| As time | 680 seconds = 11 min 20 s |
Is 680 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (680 ÷ 2 = 340) | 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 (680 ÷ 4 = 170) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (680 ÷ 5 = 136) | 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 | 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 (680 ÷ 8 = 85) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 5) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (680 ÷ 10 = 68) | 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 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 680 a prime number?
No. 680 = × 5 × 17, so it is divisible by 2.
What are the factors of 680?
1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, 680.
What is 680 in binary?
1010101000 (hexadecimal 2A8, octal 1250).
What is the square root of 680?
About 26.0768, exactly 2√170.
What is 680 in Roman numerals?
DCLXXX.
Is 680 divisible by 3?
No. Its digits add up to 14, which is not a multiple of 3.
What is special about the number 680?
680 is a happy number: repeatedly adding the squares of its digits reaches 1.