The number 59136
59136 is a composite number with 72 divisors. Its prime factorisation is × 3 × 7 × 11. Divisors (72): 1, 2, 3, 4, 6, 7, 8, 11, 12, 14, 16, 21, 22, 24, 28, 32 … 59136.
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How to work it out
- 1
What is special about 59136: a Harshad number: divisible by its digit sum 24.
- 2
59136 is composite. Its prime factorisation is
- 3
The divisors add up to 196224; without 59136 itself that is 137088, so 59136 is abundant (137088 is more than 59136). Euler's totient φ(59136) = 15360 numbers up to 59136 share no factor with it.
- 4
The digits of 59136 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 135 steps to reach 1.
LaTeX source of the formulas on this page
\[ 59136 = 2^{8} \times 3 \times 7 \times 11 \]59136 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 72 |
| Sum of divisors | 196224 |
| Euler totient φ(n) | 15360 |
| Square | 3497066496 |
| Cube | 206802524307456 |
| Square root | 243.178946 (= 16√231) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 135 |
| Scientific notation | 5.9136 × |
59136 in other forms
| Form | Value |
|---|---|
| In words | fifty-nine thousand one hundred and thirty-six |
| Binary (base 2) | 1110011100000000 |
| Octal (base 8) | 163400 |
| Hexadecimal (base 16) | E700 |
| Base 3 | 10000010020 |
| As time | 59136 seconds = 16 h 25 min 36 s |
Is 59136 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (59136 ÷ 2 = 29568) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (59136 ÷ 3 = 19712) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (59136 ÷ 4 = 14784) | 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 | Yes (59136 ÷ 6 = 9856) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (59136 ÷ 7 = 8448) | 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 (59136 ÷ 8 = 7392) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | 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 | Yes (59136 ÷ 11 = 5376) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (59136 ÷ 12 = 4928) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 59136 a prime number?
No. 59136 = × 3 × 7 × 11, so it is divisible by 2.
What are the factors of 59136?
1, 2, 3, 4, 6, 7, 8, 11, 12, 14, 16, 21, 22, 24, 28, 32, 33, 42, 44, 48, 56, 64, 66, 77, 84, 88, 96, 112, 128, 132, 154, 168, 176, 192, 224, 231, 256, 264, 308, 336, 352, 384, 448, 462, 528, 616, 672, 704, 768, 896, 924, 1056, 1232, 1344, 1408, 1792, 1848, 2112, 2464, 2688, 2816, 3696, 4224, 4928, 5376, 7392, 8448, 9856, 14784, 19712, 29568, 59136.
What is 59136 in binary?
1110011100000000 (hexadecimal E700, octal 163400).
What is the square root of 59136?
About 243.1789, exactly 16√231.
Is 59136 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 59136?
59136 is a Harshad number: divisible by its digit sum 24.