The number 47280
47280 is a composite number with 40 divisors. Its prime factorisation is × 3 × 5 × 197. Divisors (40): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48 … 47280.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 47280: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
47280 is composite. Its prime factorisation is
- 3
The divisors add up to 147312; without 47280 itself that is 100032, so 47280 is abundant (100032 is more than 47280). Euler's totient φ(47280) = 12544 numbers up to 47280 share no factor with it.
- 4
The digits of 47280 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
\[ 47280 = 2^{4} \times 3 \times 5 \times 197 \]47280 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 147312 |
| Euler totient φ(n) | 12544 |
| Square | 2235398400 |
| Cube | 105689636352000 |
| Square root | 217.439647 (= 4√2955) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 145 |
| Scientific notation | 4.728 × |
47280 in other forms
| Form | Value |
|---|---|
| In words | forty-seven thousand two hundred and eighty |
| Binary (base 2) | 1011100010110000 |
| Octal (base 8) | 134260 |
| Hexadecimal (base 16) | B8B0 |
| Base 3 | 2101212010 |
| As time | 47280 seconds = 13 h 8 min 0 s |
Is 47280 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (47280 ÷ 2 = 23640) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (47280 ÷ 3 = 15760) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (47280 ÷ 4 = 11820) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (47280 ÷ 5 = 9456) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (47280 ÷ 6 = 7880) | 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 (47280 ÷ 8 = 5910) | 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 (47280 ÷ 10 = 4728) | 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 | Yes (47280 ÷ 12 = 3940) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 47280 a prime number?
No. 47280 = × 3 × 5 × 197, so it is divisible by 2.
What are the factors of 47280?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 197, 240, 394, 591, 788, 985, 1182, 1576, 1970, 2364, 2955, 3152, 3940, 4728, 5910, 7880, 9456, 11820, 15760, 23640, 47280.
What is 47280 in binary?
1011100010110000 (hexadecimal B8B0, octal 134260).
What is the square root of 47280?
About 217.4396, exactly 4√2955.
Is 47280 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 47280?
47280 is a happy number: repeatedly adding the squares of its digits reaches 1.