The number 1776
1776 is a composite number with 20 divisors. Its prime factorisation is × 3 × 37. Divisors (20): 1, 2, 3, 4, 6, 8, 12, 16, 24, 37, 48, 74, 111, 148, 222, 296 … 1776.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
1776 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
1776 is composite. Its prime factorisation is
- 3
The divisors add up to 4712; without 1776 itself that is 2936, so 1776 is abundant (2936 is more than 1776). Euler's totient φ(1776) = 576 numbers up to 1776 share no factor with it.
- 4
The digits of 1776 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 73 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1776 = 2^{4} \times 3 \times 37 \]1776 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 4712 |
| Euler totient φ(n) | 576 |
| Square | 3154176 |
| Cube | 5601816576 |
| Square root | 42.142615 (= 4√111) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 73 |
| Scientific notation | 1.776 × |
1776 in other forms
| Form | Value |
|---|---|
| In words | one thousand seven hundred and seventy-six |
| Roman numerals | MDCCLXXVI |
| Binary (base 2) | 11011110000 |
| Octal (base 8) | 3360 |
| Hexadecimal (base 16) | 6F0 |
| Base 3 | 2102210 |
| As time | 1776 seconds = 29 min 36 s |
Is 1776 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1776 ÷ 2 = 888) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (1776 ÷ 3 = 592) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (1776 ÷ 4 = 444) | 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 (1776 ÷ 6 = 296) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (1776 ÷ 8 = 222) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | 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 (1776 ÷ 12 = 148) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1776 a prime number?
No. 1776 = × 3 × 37, so it is divisible by 2.
What are the factors of 1776?
1, 2, 3, 4, 6, 8, 12, 16, 24, 37, 48, 74, 111, 148, 222, 296, 444, 592, 888, 1776.
What is 1776 in binary?
11011110000 (hexadecimal 6F0, octal 3360).
What is the square root of 1776?
About 42.1426, exactly 4√111.
What is 1776 in Roman numerals?
MDCCLXXVI.
Is 1776 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 1776?
It is a composite number with 20 divisors.