The number 3984
3984 is a composite number with 20 divisors. Its prime factorisation is × 3 × 83. Divisors (20): 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 83, 166, 249, 332, 498, 664 … 3984.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 3984: a Harshad number: divisible by its digit sum 24.
- 2
3984 is composite. Its prime factorisation is
- 3
The divisors add up to 10416; without 3984 itself that is 6432, so 3984 is abundant (6432 is more than 3984). Euler's totient φ(3984) = 1312 numbers up to 3984 share no factor with it.
- 4
The digits of 3984 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 51 steps to reach 1.
LaTeX source of the formulas on this page
\[ 3984 = 2^{4} \times 3 \times 83 \]3984 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 10416 |
| Euler totient φ(n) | 1312 |
| Square | 15872256 |
| Cube | 63235067904 |
| Square root | 63.118935 (= 4√249) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 51 |
| Scientific notation | 3.984 × |
3984 in other forms
| Form | Value |
|---|---|
| In words | three thousand nine hundred and eighty-four |
| Roman numerals | MMMCMLXXXIV |
| Binary (base 2) | 111110010000 |
| Octal (base 8) | 7620 |
| Hexadecimal (base 16) | F90 |
| Base 3 | 12110120 |
| As time | 3984 seconds = 1 h 6 min 24 s |
Is 3984 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (3984 ÷ 2 = 1992) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (3984 ÷ 3 = 1328) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (3984 ÷ 4 = 996) | 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 (3984 ÷ 6 = 664) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 (3984 ÷ 8 = 498) | 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 | No (remainder 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (3984 ÷ 12 = 332) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 3984 a prime number?
No. 3984 = × 3 × 83, so it is divisible by 2.
What are the factors of 3984?
1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 83, 166, 249, 332, 498, 664, 996, 1328, 1992, 3984.
What is 3984 in binary?
111110010000 (hexadecimal F90, octal 7620).
What is the square root of 3984?
About 63.1189, exactly 4√249.
What is 3984 in Roman numerals?
MMMCMLXXXIV.
Is 3984 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 3984?
3984 is a Harshad number: divisible by its digit sum 24.