The number 26400
26400 is a composite number with 72 divisors. Its prime factorisation is × 3 × × 11. Divisors (72): 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 16, 20, 22, 24, 25 … 26400.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 26400: a Harshad number: divisible by its digit sum 12.
- 2
26400 is composite. Its prime factorisation is
- 3
The divisors add up to 93744; without 26400 itself that is 67344, so 26400 is abundant (67344 is more than 26400). Euler's totient φ(26400) = 6400 numbers up to 26400 share no factor with it.
- 4
The digits of 26400 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 139 steps to reach 1.
LaTeX source of the formulas on this page
\[ 26400 = 2^{5} \times 3 \times 5^{2} \times 11 \]26400 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 72 |
| Sum of divisors | 93744 |
| Euler totient φ(n) | 6400 |
| Square | 696960000 |
| Cube | 18399744000000 |
| Square root | 162.480768 (= 20√66) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 139 |
| Scientific notation | 2.64 × |
26400 in other forms
| Form | Value |
|---|---|
| In words | twenty-six thousand four hundred |
| Binary (base 2) | 110011100100000 |
| Octal (base 8) | 63440 |
| Hexadecimal (base 16) | 6720 |
| Base 3 | 1100012210 |
| As time | 26400 seconds = 7 h 20 min 0 s |
Is 26400 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (26400 ÷ 2 = 13200) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (26400 ÷ 3 = 8800) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (26400 ÷ 4 = 6600) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (26400 ÷ 5 = 5280) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (26400 ÷ 6 = 4400) | 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 (26400 ÷ 8 = 3300) | 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 | Yes (26400 ÷ 10 = 2640) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (26400 ÷ 11 = 2400) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (26400 ÷ 12 = 2200) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 26400 a prime number?
No. 26400 = × 3 × × 11, so it is divisible by 2.
What are the factors of 26400?
1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 16, 20, 22, 24, 25, 30, 32, 33, 40, 44, 48, 50, 55, 60, 66, 75, 80, 88, 96, 100, 110, 120, 132, 150, 160, 165, 176, 200, 220, 240, 264, 275, 300, 330, 352, 400, 440, 480, 528, 550, 600, 660, 800, 825, 880, 1056, 1100, 1200, 1320, 1650, 1760, 2200, 2400, 2640, 3300, 4400, 5280, 6600, 8800, 13200, 26400.
What is 26400 in binary?
110011100100000 (hexadecimal 6720, octal 63440).
What is the square root of 26400?
About 162.4808, exactly 20√66.
Is 26400 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 26400?
26400 is a Harshad number: divisible by its digit sum 12.