The number 1780
1780 is a composite number with 12 divisors. Its prime factorisation is × 5 × 89. Divisors (12): 1, 2, 4, 5, 10, 20, 89, 178, 356, 445, 890, 1780.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
1780 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
1780 is composite. Its prime factorisation is
- 3
The divisors add up to 3780; without 1780 itself that is 2000, so 1780 is abundant (2000 is more than 1780). Euler's totient φ(1780) = 704 numbers up to 1780 share no factor with it.
- 4
The digits of 1780 add up to 16, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 73 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1780 = 2^{2} \times 5 \times 89 \]1780 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 3780 |
| Euler totient φ(n) | 704 |
| Square | 3168400 |
| Cube | 5639752000 |
| Square root | 42.190046 (= 2√445) |
| Digit sum / digital root | 16 / 7 |
| Collatz steps to 1 | 73 |
| Scientific notation | 1.78 × |
1780 in other forms
| Form | Value |
|---|---|
| In words | one thousand seven hundred and eighty |
| Roman numerals | MDCCLXXX |
| Binary (base 2) | 11011110100 |
| Octal (base 8) | 3364 |
| Hexadecimal (base 16) | 6F4 |
| Base 3 | 2102221 |
| As time | 1780 seconds = 29 min 40 s |
Is 1780 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1780 ÷ 2 = 890) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (1780 ÷ 4 = 445) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (1780 ÷ 5 = 356) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 7) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (1780 ÷ 10 = 178) | 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 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1780 a prime number?
No. 1780 = × 5 × 89, so it is divisible by 2.
What are the factors of 1780?
1, 2, 4, 5, 10, 20, 89, 178, 356, 445, 890, 1780.
What is 1780 in binary?
11011110100 (hexadecimal 6F4, octal 3364).
What is the square root of 1780?
About 42.1900, exactly 2√445.
What is 1780 in Roman numerals?
MDCCLXXX.
Is 1780 divisible by 3?
No. Its digits add up to 16, which is not a multiple of 3.
What is special about the number 1780?
It is a composite number with 12 divisors.