The number 1782
1782 is a composite number with 20 divisors. Its prime factorisation is 2 × × 11. Divisors (20): 1, 2, 3, 6, 9, 11, 18, 22, 27, 33, 54, 66, 81, 99, 162, 198 … 1782.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1782: a Harshad number: divisible by its digit sum 18.
- 2
1782 is composite. Its prime factorisation is
- 3
The divisors add up to 4356; without 1782 itself that is 2574, so 1782 is abundant (2574 is more than 1782). Euler's totient φ(1782) = 540 numbers up to 1782 share no factor with it.
- 4
The digits of 1782 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 47 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1782 = 2 \times 3^{4} \times 11 \]1782 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 4356 |
| Euler totient φ(n) | 540 |
| Square | 3175524 |
| Cube | 5658783768 |
| Square root | 42.213742 (= 9√22) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 47 |
| Scientific notation | 1.782 × |
1782 in other forms
| Form | Value |
|---|---|
| In words | one thousand seven hundred and eighty-two |
| Roman numerals | MDCCLXXXII |
| Binary (base 2) | 11011110110 |
| Octal (base 8) | 3366 |
| Hexadecimal (base 16) | 6F6 |
| Base 3 | 2110000 |
| As time | 1782 seconds = 29 min 42 s |
Is 1782 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1782 ÷ 2 = 891) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (1782 ÷ 3 = 594) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | 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 (1782 ÷ 6 = 297) | 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 6) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (1782 ÷ 9 = 198) | 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 (1782 ÷ 11 = 162) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1782 a prime number?
No. 1782 = 2 × × 11, so it is divisible by 2.
What are the factors of 1782?
1, 2, 3, 6, 9, 11, 18, 22, 27, 33, 54, 66, 81, 99, 162, 198, 297, 594, 891, 1782.
What is 1782 in binary?
11011110110 (hexadecimal 6F6, octal 3366).
What is the square root of 1782?
About 42.2137, exactly 9√22.
What is 1782 in Roman numerals?
MDCCLXXXII.
Is 1782 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 1782?
1782 is a Harshad number: divisible by its digit sum 18.