The number 3968
3968 is a composite number with 16 divisors. Its prime factorisation is × 31. Divisors (16): 1, 2, 4, 8, 16, 31, 32, 62, 64, 124, 128, 248, 496, 992, 1984, 3968.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 3968: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
3968 is composite. Its prime factorisation is
- 3
The divisors add up to 8160; without 3968 itself that is 4192, so 3968 is abundant (4192 is more than 3968). Euler's totient φ(3968) = 1920 numbers up to 3968 share no factor with it.
- 4
The digits of 3968 add up to 26, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 113 steps to reach 1.
LaTeX source of the formulas on this page
\[ 3968 = 2^{7} \times 31 \]3968 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 8160 |
| Euler totient φ(n) | 1920 |
| Square | 15745024 |
| Cube | 62476255232 |
| Square root | 62.992063 (= 8√62) |
| Digit sum / digital root | 26 / 8 |
| Collatz steps to 1 | 113 |
| Scientific notation | 3.968 × |
3968 in other forms
| Form | Value |
|---|---|
| In words | three thousand nine hundred and sixty-eight |
| Roman numerals | MMMCMLXVIII |
| Binary (base 2) | 111110000000 |
| Octal (base 8) | 7600 |
| Hexadecimal (base 16) | F80 |
| Base 3 | 12102222 |
| As time | 3968 seconds = 1 h 6 min 8 s |
Is 3968 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (3968 ÷ 2 = 1984) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (3968 ÷ 4 = 992) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 2) | 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 | Yes (3968 ÷ 8 = 496) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 8) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 3968 a prime number?
No. 3968 = × 31, so it is divisible by 2.
What are the factors of 3968?
1, 2, 4, 8, 16, 31, 32, 62, 64, 124, 128, 248, 496, 992, 1984, 3968.
What is 3968 in binary?
111110000000 (hexadecimal F80, octal 7600).
What is the square root of 3968?
About 62.9921, exactly 8√62.
What is 3968 in Roman numerals?
MMMCMLXVIII.
Is 3968 divisible by 3?
No. Its digits add up to 26, which is not a multiple of 3.
What is special about the number 3968?
3968 is a happy number: repeatedly adding the squares of its digits reaches 1.