The number 2688
2688 is a composite number with 32 divisors. Its prime factorisation is × 3 × 7. Divisors (32): 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48 … 2688.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 2688: a Harshad number: divisible by its digit sum 24.
- 2
2688 is composite. Its prime factorisation is
- 3
The divisors add up to 8160; without 2688 itself that is 5472, so 2688 is abundant (5472 is more than 2688). Euler's totient φ(2688) = 768 numbers up to 2688 share no factor with it.
- 4
The digits of 2688 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 14 steps to reach 1.
LaTeX source of the formulas on this page
\[ 2688 = 2^{7} \times 3 \times 7 \]2688 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 8160 |
| Euler totient φ(n) | 768 |
| Square | 7225344 |
| Cube | 19421724672 |
| Square root | 51.845926 (= 8√42) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 14 |
| Scientific notation | 2.688 × |
2688 in other forms
| Form | Value |
|---|---|
| In words | two thousand six hundred and eighty-eight |
| Roman numerals | MMDCLXXXVIII |
| Binary (base 2) | 101010000000 |
| Octal (base 8) | 5200 |
| Hexadecimal (base 16) | A80 |
| Base 3 | 10200120 |
| As time | 2688 seconds = 44 min 48 s |
Is 2688 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (2688 ÷ 2 = 1344) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (2688 ÷ 3 = 896) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (2688 ÷ 4 = 672) | 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 (2688 ÷ 6 = 448) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (2688 ÷ 7 = 384) | 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 (2688 ÷ 8 = 336) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | 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 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (2688 ÷ 12 = 224) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 2688 a prime number?
No. 2688 = × 3 × 7, so it is divisible by 2.
What are the factors of 2688?
1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 64, 84, 96, 112, 128, 168, 192, 224, 336, 384, 448, 672, 896, 1344, 2688.
What is 2688 in binary?
101010000000 (hexadecimal A80, octal 5200).
What is the square root of 2688?
About 51.8459, exactly 8√42.
What is 2688 in Roman numerals?
MMDCLXXXVIII.
Is 2688 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 2688?
2688 is a Harshad number: divisible by its digit sum 24.