The number 46560
46560 is a composite number with 48 divisors. Its prime factorisation is × 3 × 5 × 97. Divisors (48): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40 … 46560.
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How to work it out
- 1
46560 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
46560 is composite. Its prime factorisation is
- 3
The divisors add up to 148176; without 46560 itself that is 101616, so 46560 is abundant (101616 is more than 46560). Euler's totient φ(46560) = 12288 numbers up to 46560 share no factor with it.
- 4
The digits of 46560 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 145 steps to reach 1.
LaTeX source of the formulas on this page
\[ 46560 = 2^{5} \times 3 \times 5 \times 97 \]46560 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 148176 |
| Euler totient φ(n) | 12288 |
| Square | 2167833600 |
| Cube | 100934332416000 |
| Square root | 215.777663 (= 4√2910) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 145 |
| Scientific notation | 4.656 × |
46560 in other forms
| Form | Value |
|---|---|
| In words | forty-six thousand five hundred and sixty |
| Binary (base 2) | 1011010111100000 |
| Octal (base 8) | 132740 |
| Hexadecimal (base 16) | B5E0 |
| Base 3 | 2100212110 |
| As time | 46560 seconds = 12 h 56 min 0 s |
Is 46560 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (46560 ÷ 2 = 23280) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (46560 ÷ 3 = 15520) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (46560 ÷ 4 = 11640) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (46560 ÷ 5 = 9312) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (46560 ÷ 6 = 7760) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 (46560 ÷ 8 = 5820) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (46560 ÷ 10 = 4656) | 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 | Yes (46560 ÷ 12 = 3880) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 46560 a prime number?
No. 46560 = × 3 × 5 × 97, so it is divisible by 2.
What are the factors of 46560?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 97, 120, 160, 194, 240, 291, 388, 480, 485, 582, 776, 970, 1164, 1455, 1552, 1940, 2328, 2910, 3104, 3880, 4656, 5820, 7760, 9312, 11640, 15520, 23280, 46560.
What is 46560 in binary?
1011010111100000 (hexadecimal B5E0, octal 132740).
What is the square root of 46560?
About 215.7777, exactly 4√2910.
Is 46560 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 46560?
It is a composite number with 48 divisors.