The number 3780
3780 is a composite number with 48 divisors. Its prime factorisation is × × 5 × 7. Divisors (48): 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 27 … 3780.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 3780: a Harshad number: divisible by its digit sum 18.
- 2
3780 is composite. Its prime factorisation is
- 3
The divisors add up to 13440; without 3780 itself that is 9660, so 3780 is abundant (9660 is more than 3780). Euler's totient φ(3780) = 864 numbers up to 3780 share no factor with it.
- 4
The digits of 3780 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 38 steps to reach 1.
LaTeX source of the formulas on this page
\[ 3780 = 2^{2} \times 3^{3} \times 5 \times 7 \]3780 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 13440 |
| Euler totient φ(n) | 864 |
| Square | 14288400 |
| Cube | 54010152000 |
| Square root | 61.481705 (= 6√105) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 38 |
| Scientific notation | 3.78 × |
3780 in other forms
| Form | Value |
|---|---|
| In words | three thousand seven hundred and eighty |
| Roman numerals | MMMDCCLXXX |
| Binary (base 2) | 111011000100 |
| Octal (base 8) | 7304 |
| Hexadecimal (base 16) | EC4 |
| Base 3 | 12012000 |
| As time | 3780 seconds = 1 h 3 min 0 s |
Is 3780 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (3780 ÷ 2 = 1890) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (3780 ÷ 3 = 1260) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (3780 ÷ 4 = 945) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (3780 ÷ 5 = 756) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (3780 ÷ 6 = 630) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (3780 ÷ 7 = 540) | 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 | Yes (3780 ÷ 9 = 420) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (3780 ÷ 10 = 378) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (3780 ÷ 12 = 315) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 3780 a prime number?
No. 3780 = × × 5 × 7, so it is divisible by 2.
What are the factors of 3780?
1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 27, 28, 30, 35, 36, 42, 45, 54, 60, 63, 70, 84, 90, 105, 108, 126, 135, 140, 180, 189, 210, 252, 270, 315, 378, 420, 540, 630, 756, 945, 1260, 1890, 3780.
What is 3780 in binary?
111011000100 (hexadecimal EC4, octal 7304).
What is the square root of 3780?
About 61.4817, exactly 6√105.
What is 3780 in Roman numerals?
MMMDCCLXXX.
Is 3780 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 3780?
3780 is a Harshad number: divisible by its digit sum 18.