The number 4160
4160 is a composite number with 28 divisors. Its prime factorisation is × 5 × 13. Divisors (28): 1, 2, 4, 5, 8, 10, 13, 16, 20, 26, 32, 40, 52, 64, 65, 80 … 4160.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
4160 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
4160 is composite. Its prime factorisation is
- 3
The divisors add up to 10668; without 4160 itself that is 6508, so 4160 is abundant (6508 is more than 4160). Euler's totient φ(4160) = 1536 numbers up to 4160 share no factor with it.
- 4
The digits of 4160 add up to 11, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 33 steps to reach 1.
LaTeX source of the formulas on this page
\[ 4160 = 2^{6} \times 5 \times 13 \]4160 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 28 |
| Sum of divisors | 10668 |
| Euler totient φ(n) | 1536 |
| Square | 17305600 |
| Cube | 71991296000 |
| Square root | 64.498062 (= 8√65) |
| Digit sum / digital root | 11 / 2 |
| Collatz steps to 1 | 33 |
| Scientific notation | 4.16 × |
4160 in other forms
| Form | Value |
|---|---|
| In words | four thousand one hundred and sixty |
| Binary (base 2) | 1000001000000 |
| Octal (base 8) | 10100 |
| Hexadecimal (base 16) | 1040 |
| Base 3 | 12201002 |
| As time | 4160 seconds = 1 h 9 min 20 s |
Is 4160 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (4160 ÷ 2 = 2080) | 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 (4160 ÷ 4 = 1040) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (4160 ÷ 5 = 832) | 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 2) | 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 (4160 ÷ 8 = 520) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 2) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (4160 ÷ 10 = 416) | 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 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 4160 a prime number?
No. 4160 = × 5 × 13, so it is divisible by 2.
What are the factors of 4160?
1, 2, 4, 5, 8, 10, 13, 16, 20, 26, 32, 40, 52, 64, 65, 80, 104, 130, 160, 208, 260, 320, 416, 520, 832, 1040, 2080, 4160.
What is 4160 in binary?
1000001000000 (hexadecimal 1040, octal 10100).
What is the square root of 4160?
About 64.4981, exactly 8√65.
Is 4160 divisible by 3?
No. Its digits add up to 11, which is not a multiple of 3.
What is special about the number 4160?
It is a composite number with 28 divisors.