The number 66400
66400 is a composite number with 36 divisors. Its prime factorisation is × × 83. Divisors (36): 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 83, 100, 160 … 66400.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 66400: a Harshad number: divisible by its digit sum 16.
- 2
66400 is composite. Its prime factorisation is
- 3
The divisors add up to 164052; without 66400 itself that is 97652, so 66400 is abundant (97652 is more than 66400). Euler's totient φ(66400) = 26240 numbers up to 66400 share no factor with it.
- 4
The digits of 66400 add up to 16, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 99 steps to reach 1.
LaTeX source of the formulas on this page
\[ 66400 = 2^{5} \times 5^{2} \times 83 \]66400 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 164052 |
| Euler totient φ(n) | 26240 |
| Square | 4408960000 |
| Cube | 292754944000000 |
| Square root | 257.681975 (= 20√166) |
| Digit sum / digital root | 16 / 7 |
| Collatz steps to 1 | 99 |
| Scientific notation | 6.64 × |
66400 in other forms
| Form | Value |
|---|---|
| In words | sixty-six thousand four hundred |
| Binary (base 2) | 10000001101100000 |
| Octal (base 8) | 201540 |
| Hexadecimal (base 16) | 10360 |
| Base 3 | 10101002021 |
| As time | 66400 seconds = 18 h 26 min 40 s |
Is 66400 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (66400 ÷ 2 = 33200) | 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 (66400 ÷ 4 = 16600) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (66400 ÷ 5 = 13280) | 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 5) | 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 (66400 ÷ 8 = 8300) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (66400 ÷ 10 = 6640) | 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 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 66400 a prime number?
No. 66400 = × × 83, so it is divisible by 2.
What are the factors of 66400?
1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 83, 100, 160, 166, 200, 332, 400, 415, 664, 800, 830, 1328, 1660, 2075, 2656, 3320, 4150, 6640, 8300, 13280, 16600, 33200, 66400.
What is 66400 in binary?
10000001101100000 (hexadecimal 10360, octal 201540).
What is the square root of 66400?
About 257.6820, exactly 20√166.
Is 66400 divisible by 3?
No. Its digits add up to 16, which is not a multiple of 3.
What is special about the number 66400?
66400 is a Harshad number: divisible by its digit sum 16.