The number 12996
12996 is a perfect square (114²). Its prime factorisation is × × . Divisors (27): 1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228 … 12996.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 12996: a perfect square (114²); a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
12996 is composite. Its prime factorisation is
- 3
The divisors add up to 34671; without 12996 itself that is 21675, so 12996 is abundant (21675 is more than 12996). Euler's totient φ(12996) = 4104 numbers up to 12996 share no factor with it.
- 4
The digits of 12996 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 138 steps to reach 1.
LaTeX source of the formulas on this page
\[ 12996 = 2^{2} \times 3^{2} \times 19^{2} \]12996 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 27 |
| Sum of divisors | 34671 |
| Euler totient φ(n) | 4104 |
| Square | 168896016 |
| Cube | 2194972623936 |
| Square root | 114 |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 138 |
| Scientific notation | 1.2996 × |
| Perfect power |
12996 in other forms
| Form | Value |
|---|---|
| In words | twelve thousand nine hundred and ninety-six |
| Binary (base 2) | 11001011000100 |
| Octal (base 8) | 31304 |
| Hexadecimal (base 16) | 32C4 |
| Base 3 | 122211100 |
| As time | 12996 seconds = 3 h 36 min 36 s |
Is 12996 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (12996 ÷ 2 = 6498) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (12996 ÷ 3 = 4332) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (12996 ÷ 4 = 3249) | 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 (12996 ÷ 6 = 2166) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (12996 ÷ 9 = 1444) | 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 | No (remainder 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (12996 ÷ 12 = 1083) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 12996 a prime number?
No. 12996 = × × , so it is divisible by 2.
What are the factors of 12996?
1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, 361, 684, 722, 1083, 1444, 2166, 3249, 4332, 6498, 12996.
What is 12996 in binary?
11001011000100 (hexadecimal 32C4, octal 31304).
What is the square root of 12996?
114, because 114 × 114 = 12996.
Is 12996 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 12996?
12996 is a perfect square (114²); a happy number: repeatedly adding the squares of its digits reaches 1.