The number 3840
3840 is a composite number with 36 divisors. Its prime factorisation is × 3 × 5. Divisors (36): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40 … 3840.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 3840: a Harshad number: divisible by its digit sum 15.
- 2
3840 is composite. Its prime factorisation is
- 3
The divisors add up to 12264; without 3840 itself that is 8424, so 3840 is abundant (8424 is more than 3840). Euler's totient φ(3840) = 1024 numbers up to 3840 share no factor with it.
- 4
The digits of 3840 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 25 steps to reach 1.
LaTeX source of the formulas on this page
\[ 3840 = 2^{8} \times 3 \times 5 \]3840 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 12264 |
| Euler totient φ(n) | 1024 |
| Square | 14745600 |
| Cube | 56623104000 |
| Square root | 61.967734 (= 16√15) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 25 |
| Scientific notation | 3.84 × |
3840 in other forms
| Form | Value |
|---|---|
| In words | three thousand eight hundred and forty |
| Roman numerals | MMMDCCCXL |
| Binary (base 2) | 111100000000 |
| Octal (base 8) | 7400 |
| Hexadecimal (base 16) | F00 |
| Base 3 | 12021020 |
| As time | 3840 seconds = 1 h 4 min 0 s |
Is 3840 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (3840 ÷ 2 = 1920) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (3840 ÷ 3 = 1280) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (3840 ÷ 4 = 960) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (3840 ÷ 5 = 768) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (3840 ÷ 6 = 640) | 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 | Yes (3840 ÷ 8 = 480) | 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 | Yes (3840 ÷ 10 = 384) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (3840 ÷ 12 = 320) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 3840 a prime number?
No. 3840 = × 3 × 5, so it is divisible by 2.
What are the factors of 3840?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 128, 160, 192, 240, 256, 320, 384, 480, 640, 768, 960, 1280, 1920, 3840.
What is 3840 in binary?
111100000000 (hexadecimal F00, octal 7400).
What is the square root of 3840?
About 61.9677, exactly 16√15.
What is 3840 in Roman numerals?
MMMDCCCXL.
Is 3840 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 3840?
3840 is a Harshad number: divisible by its digit sum 15.