The number 3864
3864 is a composite number with 32 divisors. Its prime factorisation is × 3 × 7 × 23. Divisors (32): 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 23, 24, 28, 42, 46, 56 … 3864.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 3864: a Harshad number: divisible by its digit sum 21.
- 2
3864 is composite. Its prime factorisation is
- 3
The divisors add up to 11520; without 3864 itself that is 7656, so 3864 is abundant (7656 is more than 3864). Euler's totient φ(3864) = 1056 numbers up to 3864 share no factor with it.
- 4
The digits of 3864 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 25 steps to reach 1.
LaTeX source of the formulas on this page
\[ 3864 = 2^{3} \times 3 \times 7 \times 23 \]3864 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 11520 |
| Euler totient φ(n) | 1056 |
| Square | 14930496 |
| Cube | 57691436544 |
| Square root | 62.161081 (= 2√966) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 25 |
| Scientific notation | 3.864 × |
3864 in other forms
| Form | Value |
|---|---|
| In words | three thousand eight hundred and sixty-four |
| Roman numerals | MMMDCCCLXIV |
| Binary (base 2) | 111100011000 |
| Octal (base 8) | 7430 |
| Hexadecimal (base 16) | F18 |
| Base 3 | 12022010 |
| As time | 3864 seconds = 1 h 4 min 24 s |
Is 3864 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (3864 ÷ 2 = 1932) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (3864 ÷ 3 = 1288) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (3864 ÷ 4 = 966) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (3864 ÷ 6 = 644) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (3864 ÷ 7 = 552) | 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 (3864 ÷ 8 = 483) | 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 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (3864 ÷ 12 = 322) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 3864 a prime number?
No. 3864 = × 3 × 7 × 23, so it is divisible by 2.
What are the factors of 3864?
1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 23, 24, 28, 42, 46, 56, 69, 84, 92, 138, 161, 168, 184, 276, 322, 483, 552, 644, 966, 1288, 1932, 3864.
What is 3864 in binary?
111100011000 (hexadecimal F18, octal 7430).
What is the square root of 3864?
About 62.1611, exactly 2√966.
What is 3864 in Roman numerals?
MMMDCCCLXIV.
Is 3864 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 3864?
3864 is a Harshad number: divisible by its digit sum 21.