The number 3996
3996 is a composite number with 24 divisors. Its prime factorisation is × × 37. Divisors (24): 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 37, 54, 74, 108, 111, 148 … 3996.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 3996: a Harshad number: divisible by its digit sum 27.
- 2
3996 is composite. Its prime factorisation is
- 3
The divisors add up to 10640; without 3996 itself that is 6644, so 3996 is abundant (6644 is more than 3996). Euler's totient φ(3996) = 1296 numbers up to 3996 share no factor with it.
- 4
The digits of 3996 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 51 steps to reach 1.
LaTeX source of the formulas on this page
\[ 3996 = 2^{2} \times 3^{3} \times 37 \]3996 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 10640 |
| Euler totient φ(n) | 1296 |
| Square | 15968016 |
| Cube | 63808191936 |
| Square root | 63.213923 (= 6√111) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 51 |
| Scientific notation | 3.996 × |
3996 in other forms
| Form | Value |
|---|---|
| In words | three thousand nine hundred and ninety-six |
| Roman numerals | MMMCMXCVI |
| Binary (base 2) | 111110011100 |
| Octal (base 8) | 7634 |
| Hexadecimal (base 16) | F9C |
| Base 3 | 12111000 |
| As time | 3996 seconds = 1 h 6 min 36 s |
Is 3996 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (3996 ÷ 2 = 1998) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (3996 ÷ 3 = 1332) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (3996 ÷ 4 = 999) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (3996 ÷ 6 = 666) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 (3996 ÷ 9 = 444) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 6) | 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 (3996 ÷ 12 = 333) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 3996 a prime number?
No. 3996 = × × 37, so it is divisible by 2.
What are the factors of 3996?
1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 37, 54, 74, 108, 111, 148, 222, 333, 444, 666, 999, 1332, 1998, 3996.
What is 3996 in binary?
111110011100 (hexadecimal F9C, octal 7634).
What is the square root of 3996?
About 63.2139, exactly 6√111.
What is 3996 in Roman numerals?
MMMCMXCVI.
Is 3996 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 3996?
3996 is a Harshad number: divisible by its digit sum 27.