The number 11328
11328 is a composite number with 28 divisors. Its prime factorisation is × 3 × 59. Divisors (28): 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 59, 64, 96, 118, 177 … 11328.
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How to work it out
- 1
What is special about 11328: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
11328 is composite. Its prime factorisation is
- 3
The divisors add up to 30480; without 11328 itself that is 19152, so 11328 is abundant (19152 is more than 11328). Euler's totient φ(11328) = 3712 numbers up to 11328 share no factor with it.
- 4
The digits of 11328 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 37 steps to reach 1.
LaTeX source of the formulas on this page
\[ 11328 = 2^{6} \times 3 \times 59 \]11328 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 28 |
| Sum of divisors | 30480 |
| Euler totient φ(n) | 3712 |
| Square | 128323584 |
| Cube | 1453649559552 |
| Square root | 106.433078 (= 8√177) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 37 |
| Scientific notation | 1.1328 × |
11328 in other forms
| Form | Value |
|---|---|
| In words | eleven thousand three hundred and twenty-eight |
| Binary (base 2) | 10110001000000 |
| Octal (base 8) | 26100 |
| Hexadecimal (base 16) | 2C40 |
| Base 3 | 120112120 |
| As time | 11328 seconds = 3 h 8 min 48 s |
Is 11328 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (11328 ÷ 2 = 5664) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (11328 ÷ 3 = 3776) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (11328 ÷ 4 = 2832) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (11328 ÷ 6 = 1888) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 (11328 ÷ 8 = 1416) | 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 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (11328 ÷ 12 = 944) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 11328 a prime number?
No. 11328 = × 3 × 59, so it is divisible by 2.
What are the factors of 11328?
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 59, 64, 96, 118, 177, 192, 236, 354, 472, 708, 944, 1416, 1888, 2832, 3776, 5664, 11328.
What is 11328 in binary?
10110001000000 (hexadecimal 2C40, octal 26100).
What is the square root of 11328?
About 106.4331, exactly 8√177.
Is 11328 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 11328?
11328 is a happy number: repeatedly adding the squares of its digits reaches 1.