The number 12144
12144 is a composite number with 40 divisors. Its prime factorisation is × 3 × 11 × 23. Divisors (40): 1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 23, 24, 33, 44, 46, 48 … 12144.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 12144: a Harshad number: divisible by its digit sum 12.
- 2
12144 is composite. Its prime factorisation is
- 3
The divisors add up to 35712; without 12144 itself that is 23568, so 12144 is abundant (23568 is more than 12144). Euler's totient φ(12144) = 3520 numbers up to 12144 share no factor with it.
- 4
The digits of 12144 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 63 steps to reach 1.
LaTeX source of the formulas on this page
\[ 12144 = 2^{4} \times 3 \times 11 \times 23 \]12144 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 35712 |
| Euler totient φ(n) | 3520 |
| Square | 147476736 |
| Cube | 1790957481984 |
| Square root | 110.199819 (= 4√759) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 63 |
| Scientific notation | 1.2144 × |
12144 in other forms
| Form | Value |
|---|---|
| In words | twelve thousand one hundred and forty-four |
| Binary (base 2) | 10111101110000 |
| Octal (base 8) | 27560 |
| Hexadecimal (base 16) | 2F70 |
| Base 3 | 121122210 |
| As time | 12144 seconds = 3 h 22 min 24 s |
Is 12144 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (12144 ÷ 2 = 6072) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (12144 ÷ 3 = 4048) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (12144 ÷ 4 = 3036) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (12144 ÷ 6 = 2024) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 (12144 ÷ 8 = 1518) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (12144 ÷ 11 = 1104) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (12144 ÷ 12 = 1012) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 12144 a prime number?
No. 12144 = × 3 × 11 × 23, so it is divisible by 2.
What are the factors of 12144?
1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 23, 24, 33, 44, 46, 48, 66, 69, 88, 92, 132, 138, 176, 184, 253, 264, 276, 368, 506, 528, 552, 759, 1012, 1104, 1518, 2024, 3036, 4048, 6072, 12144.
What is 12144 in binary?
10111101110000 (hexadecimal 2F70, octal 27560).
What is the square root of 12144?
About 110.1998, exactly 4√759.
Is 12144 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 12144?
12144 is a Harshad number: divisible by its digit sum 12.