The number 12984
12984 is a composite number with 16 divisors. Its prime factorisation is × 3 × 541. Divisors (16): 1, 2, 3, 4, 6, 8, 12, 24, 541, 1082, 1623, 2164, 3246, 4328, 6492, 12984.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 12984: a Harshad number: divisible by its digit sum 24.
- 2
12984 is composite. Its prime factorisation is
- 3
The divisors add up to 32520; without 12984 itself that is 19536, so 12984 is abundant (19536 is more than 12984). Euler's totient φ(12984) = 4320 numbers up to 12984 share no factor with it.
- 4
The digits of 12984 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 138 steps to reach 1.
LaTeX source of the formulas on this page
\[ 12984 = 2^{3} \times 3 \times 541 \]12984 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 32520 |
| Euler totient φ(n) | 4320 |
| Square | 168584256 |
| Cube | 2188897979904 |
| Square root | 113.947356 (= 2√3246) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 138 |
| Scientific notation | 1.2984 × |
12984 in other forms
| Form | Value |
|---|---|
| In words | twelve thousand nine hundred and eighty-four |
| Binary (base 2) | 11001010111000 |
| Octal (base 8) | 31270 |
| Hexadecimal (base 16) | 32B8 |
| Base 3 | 122210220 |
| As time | 12984 seconds = 3 h 36 min 24 s |
Is 12984 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (12984 ÷ 2 = 6492) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (12984 ÷ 3 = 4328) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (12984 ÷ 4 = 3246) | 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 (12984 ÷ 6 = 2164) | 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 (12984 ÷ 8 = 1623) | 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 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (12984 ÷ 12 = 1082) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 12984 a prime number?
No. 12984 = × 3 × 541, so it is divisible by 2.
What are the factors of 12984?
1, 2, 3, 4, 6, 8, 12, 24, 541, 1082, 1623, 2164, 3246, 4328, 6492, 12984.
What is 12984 in binary?
11001010111000 (hexadecimal 32B8, octal 31270).
What is the square root of 12984?
About 113.9474, exactly 2√3246.
Is 12984 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 12984?
12984 is a Harshad number: divisible by its digit sum 24.