The number 3960
3960 is a composite number with 48 divisors. Its prime factorisation is × × 5 × 11. Divisors (48): 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 15, 18, 20, 22, 24 … 3960.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 3960: a Harshad number: divisible by its digit sum 18.
- 2
3960 is composite. Its prime factorisation is
- 3
The divisors add up to 14040; without 3960 itself that is 10080, so 3960 is abundant (10080 is more than 3960). Euler's totient φ(3960) = 960 numbers up to 3960 share no factor with it.
- 4
The digits of 3960 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 100 steps to reach 1.
LaTeX source of the formulas on this page
\[ 3960 = 2^{3} \times 3^{2} \times 5 \times 11 \]3960 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 14040 |
| Euler totient φ(n) | 960 |
| Square | 15681600 |
| Cube | 62099136000 |
| Square root | 62.928531 (= 6√110) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 100 |
| Scientific notation | 3.96 × |
3960 in other forms
| Form | Value |
|---|---|
| In words | three thousand nine hundred and sixty |
| Roman numerals | MMMCMLX |
| Binary (base 2) | 111101111000 |
| Octal (base 8) | 7570 |
| Hexadecimal (base 16) | F78 |
| Base 3 | 12102200 |
| As time | 3960 seconds = 1 h 6 min 0 s |
Is 3960 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (3960 ÷ 2 = 1980) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (3960 ÷ 3 = 1320) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (3960 ÷ 4 = 990) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (3960 ÷ 5 = 792) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (3960 ÷ 6 = 660) | 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 (3960 ÷ 8 = 495) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (3960 ÷ 9 = 440) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (3960 ÷ 10 = 396) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (3960 ÷ 11 = 360) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (3960 ÷ 12 = 330) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 3960 a prime number?
No. 3960 = × × 5 × 11, so it is divisible by 2.
What are the factors of 3960?
1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 15, 18, 20, 22, 24, 30, 33, 36, 40, 44, 45, 55, 60, 66, 72, 88, 90, 99, 110, 120, 132, 165, 180, 198, 220, 264, 330, 360, 396, 440, 495, 660, 792, 990, 1320, 1980, 3960.
What is 3960 in binary?
111101111000 (hexadecimal F78, octal 7570).
What is the square root of 3960?
About 62.9285, exactly 6√110.
What is 3960 in Roman numerals?
MMMCMLX.
Is 3960 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 3960?
3960 is a Harshad number: divisible by its digit sum 18.