The number 16400
16400 is a composite number with 30 divisors. Its prime factorisation is × × 41. Divisors (30): 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 41, 50, 80, 82, 100, 164 … 16400.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
16400 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
16400 is composite. Its prime factorisation is
- 3
The divisors add up to 40362; without 16400 itself that is 23962, so 16400 is abundant (23962 is more than 16400). Euler's totient φ(16400) = 6400 numbers up to 16400 share no factor with it.
- 4
The digits of 16400 add up to 11, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 40 steps to reach 1.
LaTeX source of the formulas on this page
\[ 16400 = 2^{4} \times 5^{2} \times 41 \]16400 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 30 |
| Sum of divisors | 40362 |
| Euler totient φ(n) | 6400 |
| Square | 268960000 |
| Cube | 4410944000000 |
| Square root | 128.062485 (= 20√41) |
| Digit sum / digital root | 11 / 2 |
| Collatz steps to 1 | 40 |
| Scientific notation | 1.64 × |
16400 in other forms
| Form | Value |
|---|---|
| In words | sixteen thousand four hundred |
| Binary (base 2) | 100000000010000 |
| Octal (base 8) | 40020 |
| Hexadecimal (base 16) | 4010 |
| Base 3 | 211111102 |
| As time | 16400 seconds = 4 h 33 min 20 s |
Is 16400 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (16400 ÷ 2 = 8200) | 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 (16400 ÷ 4 = 4100) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (16400 ÷ 5 = 3280) | 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 6) | 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 (16400 ÷ 8 = 2050) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 2) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (16400 ÷ 10 = 1640) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | 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 16400 a prime number?
No. 16400 = × × 41, so it is divisible by 2.
What are the factors of 16400?
1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 41, 50, 80, 82, 100, 164, 200, 205, 328, 400, 410, 656, 820, 1025, 1640, 2050, 3280, 4100, 8200, 16400.
What is 16400 in binary?
100000000010000 (hexadecimal 4010, octal 40020).
What is the square root of 16400?
About 128.0625, exactly 20√41.
Is 16400 divisible by 3?
No. Its digits add up to 11, which is not a multiple of 3.
What is special about the number 16400?
It is a composite number with 30 divisors.