The number 46080
46080 is a composite number with 66 divisors. Its prime factorisation is × × 5. Divisors (66): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30 … 46080.
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How to work it out
- 1
What is special about 46080: a Harshad number: divisible by its digit sum 18.
- 2
46080 is composite. Its prime factorisation is
- 3
The divisors add up to 159666; without 46080 itself that is 113586, so 46080 is abundant (113586 is more than 46080). Euler's totient φ(46080) = 12288 numbers up to 46080 share no factor with it.
- 4
The digits of 46080 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 26 steps to reach 1.
LaTeX source of the formulas on this page
\[ 46080 = 2^{10} \times 3^{2} \times 5 \]46080 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 66 |
| Sum of divisors | 159666 |
| Euler totient φ(n) | 12288 |
| Square | 2123366400 |
| Cube | 97844723712000 |
| Square root | 214.662526 (= 96√5) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 26 |
| Scientific notation | 4.608 × |
46080 in other forms
| Form | Value |
|---|---|
| In words | forty-six thousand and eighty |
| Binary (base 2) | 1011010000000000 |
| Octal (base 8) | 132000 |
| Hexadecimal (base 16) | B400 |
| Base 3 | 2100012200 |
| As time | 46080 seconds = 12 h 48 min 0 s |
Is 46080 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (46080 ÷ 2 = 23040) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (46080 ÷ 3 = 15360) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (46080 ÷ 4 = 11520) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (46080 ÷ 5 = 9216) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (46080 ÷ 6 = 7680) | 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 (46080 ÷ 8 = 5760) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (46080 ÷ 9 = 5120) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (46080 ÷ 10 = 4608) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (46080 ÷ 12 = 3840) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 46080 a prime number?
No. 46080 = × × 5, so it is divisible by 2.
What are the factors of 46080?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 32, 36, 40, 45, 48, 60, 64, 72, 80, 90, 96, 120, 128, 144, 160, 180, 192, 240, 256, 288, 320, 360, 384, 480, 512, 576, 640, 720, 768, 960, 1024, 1152, 1280, 1440, 1536, 1920, 2304, 2560, 2880, 3072, 3840, 4608, 5120, 5760, 7680, 9216, 11520, 15360, 23040, 46080.
What is 46080 in binary?
1011010000000000 (hexadecimal B400, octal 132000).
What is the square root of 46080?
About 214.6625, exactly 96√5.
Is 46080 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 46080?
46080 is a Harshad number: divisible by its digit sum 18.