The number 1284
1284 is a composite number with 12 divisors. Its prime factorisation is × 3 × 107. Divisors (12): 1, 2, 3, 4, 6, 12, 107, 214, 321, 428, 642, 1284.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
1284 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
1284 is composite. Its prime factorisation is
- 3
The divisors add up to 3024; without 1284 itself that is 1740, so 1284 is abundant (1740 is more than 1284). Euler's totient φ(1284) = 424 numbers up to 1284 share no factor with it.
- 4
The digits of 1284 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 26 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1284 = 2^{2} \times 3 \times 107 \]1284 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 3024 |
| Euler totient φ(n) | 424 |
| Square | 1648656 |
| Cube | 2116874304 |
| Square root | 35.832946 (= 2√321) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 26 |
| Scientific notation | 1.284 × |
1284 in other forms
| Form | Value |
|---|---|
| In words | one thousand two hundred and eighty-four |
| Roman numerals | MCCLXXXIV |
| Binary (base 2) | 10100000100 |
| Octal (base 8) | 2404 |
| Hexadecimal (base 16) | 504 |
| Base 3 | 1202120 |
| As time | 1284 seconds = 21 min 24 s |
Is 1284 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1284 ÷ 2 = 642) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (1284 ÷ 3 = 428) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (1284 ÷ 4 = 321) | 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 (1284 ÷ 6 = 214) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 | 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 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (1284 ÷ 12 = 107) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1284 a prime number?
No. 1284 = × 3 × 107, so it is divisible by 2.
What are the factors of 1284?
1, 2, 3, 4, 6, 12, 107, 214, 321, 428, 642, 1284.
What is 1284 in binary?
10100000100 (hexadecimal 504, octal 2404).
What is the square root of 1284?
About 35.8329, exactly 2√321.
What is 1284 in Roman numerals?
MCCLXXXIV.
Is 1284 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 1284?
It is a composite number with 12 divisors.