The number 12672
12672 is a composite number with 48 divisors. Its prime factorisation is × × 11. Divisors (48): 1, 2, 3, 4, 6, 8, 9, 11, 12, 16, 18, 22, 24, 32, 33, 36 … 12672.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 12672: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
12672 is composite. Its prime factorisation is
- 3
The divisors add up to 39780; without 12672 itself that is 27108, so 12672 is abundant (27108 is more than 12672). Euler's totient φ(12672) = 3840 numbers up to 12672 share no factor with it.
- 4
The digits of 12672 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 32 steps to reach 1.
LaTeX source of the formulas on this page
\[ 12672 = 2^{7} \times 3^{2} \times 11 \]12672 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 39780 |
| Euler totient φ(n) | 3840 |
| Square | 160579584 |
| Cube | 2034864488448 |
| Square root | 112.569978 (= 24√22) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 32 |
| Scientific notation | 1.2672 × |
12672 in other forms
| Form | Value |
|---|---|
| In words | twelve thousand six hundred and seventy-two |
| Binary (base 2) | 11000110000000 |
| Octal (base 8) | 30600 |
| Hexadecimal (base 16) | 3180 |
| Base 3 | 122101100 |
| As time | 12672 seconds = 3 h 31 min 12 s |
Is 12672 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (12672 ÷ 2 = 6336) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (12672 ÷ 3 = 4224) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (12672 ÷ 4 = 3168) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (12672 ÷ 6 = 2112) | 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 (12672 ÷ 8 = 1584) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (12672 ÷ 9 = 1408) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 2) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (12672 ÷ 11 = 1152) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (12672 ÷ 12 = 1056) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 12672 a prime number?
No. 12672 = × × 11, so it is divisible by 2.
What are the factors of 12672?
1, 2, 3, 4, 6, 8, 9, 11, 12, 16, 18, 22, 24, 32, 33, 36, 44, 48, 64, 66, 72, 88, 96, 99, 128, 132, 144, 176, 192, 198, 264, 288, 352, 384, 396, 528, 576, 704, 792, 1056, 1152, 1408, 1584, 2112, 3168, 4224, 6336, 12672.
What is 12672 in binary?
11000110000000 (hexadecimal 3180, octal 30600).
What is the square root of 12672?
About 112.5700, exactly 24√22.
Is 12672 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 12672?
12672 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.