The number 1296
1296 is a perfect power () and a perfect square (36²). Its prime factorisation is × . Divisors (25): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72 … 1296.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1296: a perfect power (); a perfect square (36²); a Harshad number: divisible by its digit sum 18.
- 2
1296 is composite. Its prime factorisation is
- 3
The divisors add up to 3751; without 1296 itself that is 2455, so 1296 is abundant (2455 is more than 1296). Euler's totient φ(1296) = 432 numbers up to 1296 share no factor with it.
- 4
The digits of 1296 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 26 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1296 = 2^{4} \times 3^{4} \]1296 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 25 |
| Sum of divisors | 3751 |
| Euler totient φ(n) | 432 |
| Square | 1679616 |
| Cube | 2176782336 |
| Square root | 36 |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 26 |
| Scientific notation | 1.296 × |
| Perfect power |
1296 in other forms
| Form | Value |
|---|---|
| In words | one thousand two hundred and ninety-six |
| Roman numerals | MCCXCVI |
| Binary (base 2) | 10100010000 |
| Octal (base 8) | 2420 |
| Hexadecimal (base 16) | 510 |
| Base 3 | 1210000 |
| As time | 1296 seconds = 21 min 36 s |
Is 1296 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1296 ÷ 2 = 648) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (1296 ÷ 3 = 432) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (1296 ÷ 4 = 324) | 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 (1296 ÷ 6 = 216) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 (1296 ÷ 8 = 162) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (1296 ÷ 9 = 144) | 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 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (1296 ÷ 12 = 108) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1296 a prime number?
No. 1296 = × , so it is divisible by 2.
What are the factors of 1296?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 81, 108, 144, 162, 216, 324, 432, 648, 1296.
What is 1296 in binary?
10100010000 (hexadecimal 510, octal 2420).
What is the square root of 1296?
36, because 36 × 36 = 1296.
What is 1296 in Roman numerals?
MCCXCVI.
Is 1296 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 1296?
1296 is a perfect power (); a perfect square (36²); a Harshad number: divisible by its digit sum 18.