The number 3904
3904 is a composite number with 14 divisors. Its prime factorisation is × 61. Divisors (14): 1, 2, 4, 8, 16, 32, 61, 64, 122, 244, 488, 976, 1952, 3904.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 3904: a Harshad number: divisible by its digit sum 16.
- 2
3904 is composite. Its prime factorisation is
- 3
The divisors add up to 7874; without 3904 itself that is 3970, so 3904 is abundant (3970 is more than 3904). Euler's totient φ(3904) = 1920 numbers up to 3904 share no factor with it.
- 4
The digits of 3904 add up to 16, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 25 steps to reach 1.
LaTeX source of the formulas on this page
\[ 3904 = 2^{6} \times 61 \]3904 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 14 |
| Sum of divisors | 7874 |
| Euler totient φ(n) | 1920 |
| Square | 15241216 |
| Cube | 59501707264 |
| Square root | 62.481997 (= 8√61) |
| Digit sum / digital root | 16 / 7 |
| Collatz steps to 1 | 25 |
| Scientific notation | 3.904 × |
3904 in other forms
| Form | Value |
|---|---|
| In words | three thousand nine hundred and four |
| Roman numerals | MMMCMIV |
| Binary (base 2) | 111101000000 |
| Octal (base 8) | 7500 |
| Hexadecimal (base 16) | F40 |
| Base 3 | 12100121 |
| As time | 3904 seconds = 1 h 5 min 4 s |
Is 3904 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (3904 ÷ 2 = 1952) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (3904 ÷ 4 = 976) | 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 | No (remainder 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (3904 ÷ 8 = 488) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | 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 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 3904 a prime number?
No. 3904 = × 61, so it is divisible by 2.
What are the factors of 3904?
1, 2, 4, 8, 16, 32, 61, 64, 122, 244, 488, 976, 1952, 3904.
What is 3904 in binary?
111101000000 (hexadecimal F40, octal 7500).
What is the square root of 3904?
About 62.4820, exactly 8√61.
What is 3904 in Roman numerals?
MMMCMIV.
Is 3904 divisible by 3?
No. Its digits add up to 16, which is not a multiple of 3.
What is special about the number 3904?
3904 is a Harshad number: divisible by its digit sum 16.