The number 6400
6400 is a perfect square (80²). Its prime factorisation is × . Divisors (27): 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 128 … 6400.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 6400: a perfect square (80²); a Harshad number: divisible by its digit sum 10.
- 2
6400 is composite. Its prime factorisation is
- 3
The divisors add up to 15841; without 6400 itself that is 9441, so 6400 is abundant (9441 is more than 6400). Euler's totient φ(6400) = 2560 numbers up to 6400 share no factor with it.
- 4
The digits of 6400 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 31 steps to reach 1.
LaTeX source of the formulas on this page
\[ 6400 = 2^{8} \times 5^{2} \]6400 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 27 |
| Sum of divisors | 15841 |
| Euler totient φ(n) | 2560 |
| Square | 40960000 |
| Cube | 262144000000 |
| Square root | 80 |
| Digit sum / digital root | 10 / 1 |
| Collatz steps to 1 | 31 |
| Scientific notation | 6.4 × |
| Perfect power |
6400 in other forms
| Form | Value |
|---|---|
| In words | six thousand four hundred |
| Binary (base 2) | 1100100000000 |
| Octal (base 8) | 14400 |
| Hexadecimal (base 16) | 1900 |
| Base 3 | 22210001 |
| As time | 6400 seconds = 1 h 46 min 40 s |
Is 6400 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (6400 ÷ 2 = 3200) | 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 (6400 ÷ 4 = 1600) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (6400 ÷ 5 = 1280) | 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 2) | 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 (6400 ÷ 8 = 800) | 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 | Yes (6400 ÷ 10 = 640) | 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 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 6400 a prime number?
No. 6400 = × , so it is divisible by 2.
What are the factors of 6400?
1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 128, 160, 200, 256, 320, 400, 640, 800, 1280, 1600, 3200, 6400.
What is 6400 in binary?
1100100000000 (hexadecimal 1900, octal 14400).
What is the square root of 6400?
80, because 80 × 80 = 6400.
Is 6400 divisible by 3?
No. Its digits add up to 10, which is not a multiple of 3.
What is special about the number 6400?
6400 is a perfect square (80²); a Harshad number: divisible by its digit sum 10.