The number 26880
26880 is a composite number with 72 divisors. Its prime factorisation is × 3 × 5 × 7. Divisors (72): 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24 … 26880.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 26880: a Harshad number: divisible by its digit sum 24.
- 2
26880 is composite. Its prime factorisation is
- 3
The divisors add up to 98112; without 26880 itself that is 71232, so 26880 is abundant (71232 is more than 26880). Euler's totient φ(26880) = 6144 numbers up to 26880 share no factor with it.
- 4
The digits of 26880 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 46 steps to reach 1.
LaTeX source of the formulas on this page
\[ 26880 = 2^{8} \times 3 \times 5 \times 7 \]26880 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 72 |
| Sum of divisors | 98112 |
| Euler totient φ(n) | 6144 |
| Square | 722534400 |
| Cube | 19421724672000 |
| Square root | 163.951212 (= 16√105) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 46 |
| Scientific notation | 2.688 × |
26880 in other forms
| Form | Value |
|---|---|
| In words | twenty-six thousand eight hundred and eighty |
| Binary (base 2) | 110100100000000 |
| Octal (base 8) | 64400 |
| Hexadecimal (base 16) | 6900 |
| Base 3 | 1100212120 |
| As time | 26880 seconds = 7 h 28 min 0 s |
Is 26880 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (26880 ÷ 2 = 13440) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (26880 ÷ 3 = 8960) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (26880 ÷ 4 = 6720) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (26880 ÷ 5 = 5376) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (26880 ÷ 6 = 4480) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (26880 ÷ 7 = 3840) | 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 (26880 ÷ 8 = 3360) | 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 | Yes (26880 ÷ 10 = 2688) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (26880 ÷ 12 = 2240) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 26880 a prime number?
No. 26880 = × 3 × 5 × 7, so it is divisible by 2.
What are the factors of 26880?
1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 32, 35, 40, 42, 48, 56, 60, 64, 70, 80, 84, 96, 105, 112, 120, 128, 140, 160, 168, 192, 210, 224, 240, 256, 280, 320, 336, 384, 420, 448, 480, 560, 640, 672, 768, 840, 896, 960, 1120, 1280, 1344, 1680, 1792, 1920, 2240, 2688, 3360, 3840, 4480, 5376, 6720, 8960, 13440, 26880.
What is 26880 in binary?
110100100000000 (hexadecimal 6900, octal 64400).
What is the square root of 26880?
About 163.9512, exactly 16√105.
Is 26880 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 26880?
26880 is a Harshad number: divisible by its digit sum 24.