The number 36736
36736 is a composite number with 32 divisors. Its prime factorisation is × 7 × 41. Divisors (32): 1, 2, 4, 7, 8, 14, 16, 28, 32, 41, 56, 64, 82, 112, 128, 164 … 36736.
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How to work it out
- 1
What is special about 36736: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
36736 is composite. Its prime factorisation is
- 3
The divisors add up to 85680; without 36736 itself that is 48944, so 36736 is abundant (48944 is more than 36736). Euler's totient φ(36736) = 15360 numbers up to 36736 share no factor with it.
- 4
The digits of 36736 add up to 25, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 49 steps to reach 1.
LaTeX source of the formulas on this page
\[ 36736 = 2^{7} \times 7 \times 41 \]36736 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 85680 |
| Euler totient φ(n) | 15360 |
| Square | 1349533696 |
| Cube | 49576469856256 |
| Square root | 191.666377 (= 8√574) |
| Digit sum / digital root | 25 / 7 |
| Collatz steps to 1 | 49 |
| Scientific notation | 3.6736 × |
36736 in other forms
| Form | Value |
|---|---|
| In words | thirty-six thousand seven hundred and thirty-six |
| Binary (base 2) | 1000111110000000 |
| Octal (base 8) | 107600 |
| Hexadecimal (base 16) | 8F80 |
| Base 3 | 1212101121 |
| As time | 36736 seconds = 10 h 12 min 16 s |
Is 36736 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (36736 ÷ 2 = 18368) | 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 (36736 ÷ 4 = 9184) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | 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 (36736 ÷ 7 = 5248) | 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 (36736 ÷ 8 = 4592) | 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 | No (remainder 6) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | 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 36736 a prime number?
No. 36736 = × 7 × 41, so it is divisible by 2.
What are the factors of 36736?
1, 2, 4, 7, 8, 14, 16, 28, 32, 41, 56, 64, 82, 112, 128, 164, 224, 287, 328, 448, 574, 656, 896, 1148, 1312, 2296, 2624, 4592, 5248, 9184, 18368, 36736.
What is 36736 in binary?
1000111110000000 (hexadecimal 8F80, octal 107600).
What is the square root of 36736?
About 191.6664, exactly 8√574.
Is 36736 divisible by 3?
No. Its digits add up to 25, which is not a multiple of 3.
What is special about the number 36736?
36736 is a happy number: repeatedly adding the squares of its digits reaches 1.