The number 36400
36400 is a composite number with 60 divisors. Its prime factorisation is × × 7 × 13. Divisors (60): 1, 2, 4, 5, 7, 8, 10, 13, 14, 16, 20, 25, 26, 28, 35, 40 … 36400.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 36400: a Harshad number: divisible by its digit sum 13.
- 2
36400 is composite. Its prime factorisation is
- 3
The divisors add up to 107632; without 36400 itself that is 71232, so 36400 is abundant (71232 is more than 36400). Euler's totient φ(36400) = 11520 numbers up to 36400 share no factor with it.
- 4
The digits of 36400 add up to 13, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 23 steps to reach 1.
LaTeX source of the formulas on this page
\[ 36400 = 2^{4} \times 5^{2} \times 7 \times 13 \]36400 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 60 |
| Sum of divisors | 107632 |
| Euler totient φ(n) | 11520 |
| Square | 1324960000 |
| Cube | 48228544000000 |
| Square root | 190.787840 (= 20√91) |
| Digit sum / digital root | 13 / 4 |
| Collatz steps to 1 | 23 |
| Scientific notation | 3.64 × |
36400 in other forms
| Form | Value |
|---|---|
| In words | thirty-six thousand four hundred |
| Binary (base 2) | 1000111000110000 |
| Octal (base 8) | 107060 |
| Hexadecimal (base 16) | 8E30 |
| Base 3 | 1211221011 |
| As time | 36400 seconds = 10 h 6 min 40 s |
Is 36400 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (36400 ÷ 2 = 18200) | 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 (36400 ÷ 4 = 9100) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (36400 ÷ 5 = 7280) | 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 | Yes (36400 ÷ 7 = 5200) | 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 (36400 ÷ 8 = 4550) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 4) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (36400 ÷ 10 = 3640) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | 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 36400 a prime number?
No. 36400 = × × 7 × 13, so it is divisible by 2.
What are the factors of 36400?
1, 2, 4, 5, 7, 8, 10, 13, 14, 16, 20, 25, 26, 28, 35, 40, 50, 52, 56, 65, 70, 80, 91, 100, 104, 112, 130, 140, 175, 182, 200, 208, 260, 280, 325, 350, 364, 400, 455, 520, 560, 650, 700, 728, 910, 1040, 1300, 1400, 1456, 1820, 2275, 2600, 2800, 3640, 4550, 5200, 7280, 9100, 18200, 36400.
What is 36400 in binary?
1000111000110000 (hexadecimal 8E30, octal 107060).
What is the square root of 36400?
About 190.7878, exactly 20√91.
Is 36400 divisible by 3?
No. Its digits add up to 13, which is not a multiple of 3.
What is special about the number 36400?
36400 is a Harshad number: divisible by its digit sum 13.