The number 36800
36800 is a composite number with 42 divisors. Its prime factorisation is × × 23. Divisors (42): 1, 2, 4, 5, 8, 10, 16, 20, 23, 25, 32, 40, 46, 50, 64, 80 … 36800.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 36800: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
36800 is composite. Its prime factorisation is
- 3
The divisors add up to 94488; without 36800 itself that is 57688, so 36800 is abundant (57688 is more than 36800). Euler's totient φ(36800) = 14080 numbers up to 36800 share no factor with it.
- 4
The digits of 36800 add up to 17, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 49 steps to reach 1.
LaTeX source of the formulas on this page
\[ 36800 = 2^{6} \times 5^{2} \times 23 \]36800 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 42 |
| Sum of divisors | 94488 |
| Euler totient φ(n) | 14080 |
| Square | 1354240000 |
| Cube | 49836032000000 |
| Square root | 191.833261 (= 40√23) |
| Digit sum / digital root | 17 / 8 |
| Collatz steps to 1 | 49 |
| Scientific notation | 3.68 × |
36800 in other forms
| Form | Value |
|---|---|
| In words | thirty-six thousand eight hundred |
| Binary (base 2) | 1000111111000000 |
| Octal (base 8) | 107700 |
| Hexadecimal (base 16) | 8FC0 |
| Base 3 | 1212110222 |
| As time | 36800 seconds = 10 h 13 min 20 s |
Is 36800 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (36800 ÷ 2 = 18400) | 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 (36800 ÷ 4 = 9200) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (36800 ÷ 5 = 7360) | 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 1) | 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 (36800 ÷ 8 = 4600) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 8) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (36800 ÷ 10 = 3680) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 5) | 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 36800 a prime number?
No. 36800 = × × 23, so it is divisible by 2.
What are the factors of 36800?
1, 2, 4, 5, 8, 10, 16, 20, 23, 25, 32, 40, 46, 50, 64, 80, 92, 100, 115, 160, 184, 200, 230, 320, 368, 400, 460, 575, 736, 800, 920, 1150, 1472, 1600, 1840, 2300, 3680, 4600, 7360, 9200, 18400, 36800.
What is 36800 in binary?
1000111111000000 (hexadecimal 8FC0, octal 107700).
What is the square root of 36800?
About 191.8333, exactly 40√23.
Is 36800 divisible by 3?
No. Its digits add up to 17, which is not a multiple of 3.
What is special about the number 36800?
36800 is a happy number: repeatedly adding the squares of its digits reaches 1.