The number 47520
47520 is a composite number with 96 divisors. Its prime factorisation is × × 5 × 11. Divisors (96): 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 15, 16, 18, 20, 22 … 47520.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 47520: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
47520 is composite. Its prime factorisation is
- 3
The divisors add up to 181440; without 47520 itself that is 133920, so 47520 is abundant (133920 is more than 47520). Euler's totient φ(47520) = 11520 numbers up to 47520 share no factor with it.
- 4
The digits of 47520 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 52 steps to reach 1.
LaTeX source of the formulas on this page
\[ 47520 = 2^{5} \times 3^{3} \times 5 \times 11 \]47520 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 96 |
| Sum of divisors | 181440 |
| Euler totient φ(n) | 11520 |
| Square | 2258150400 |
| Cube | 107307307008000 |
| Square root | 217.990825 (= 12√330) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 52 |
| Scientific notation | 4.752 × |
47520 in other forms
| Form | Value |
|---|---|
| In words | forty-seven thousand five hundred and twenty |
| Binary (base 2) | 1011100110100000 |
| Octal (base 8) | 134640 |
| Hexadecimal (base 16) | B9A0 |
| Base 3 | 2102012000 |
| As time | 47520 seconds = 13 h 12 min 0 s |
Is 47520 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (47520 ÷ 2 = 23760) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (47520 ÷ 3 = 15840) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (47520 ÷ 4 = 11880) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (47520 ÷ 5 = 9504) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (47520 ÷ 6 = 7920) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 (47520 ÷ 8 = 5940) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (47520 ÷ 9 = 5280) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (47520 ÷ 10 = 4752) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (47520 ÷ 11 = 4320) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (47520 ÷ 12 = 3960) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 47520 a prime number?
No. 47520 = × × 5 × 11, so it is divisible by 2.
What are the factors of 47520?
1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 15, 16, 18, 20, 22, 24, 27, 30, 32, 33, 36, 40, 44, 45, 48, 54, 55, 60, 66, 72, 80, 88, 90, 96, 99, 108, 110, 120, 132, 135, 144, 160, 165, 176, 180, 198, 216, 220, 240, 264, 270, 288, 297, 330, 352, 360, 396, 432, 440, 480, 495, 528, 540, 594, 660, 720, 792, 864, 880, 990, 1056, 1080, 1188, 1320, 1440, 1485, 1584, 1760, 1980, 2160, 2376, 2640, 2970, 3168, 3960, 4320, 4752, 5280, 5940, 7920, 9504, 11880, 15840, 23760, 47520.
What is 47520 in binary?
1011100110100000 (hexadecimal B9A0, octal 134640).
What is the square root of 47520?
About 217.9908, exactly 12√330.
Is 47520 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 47520?
47520 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.