The number 47760
47760 is a composite number with 40 divisors. Its prime factorisation is × 3 × 5 × 199. Divisors (40): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48 … 47760.
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How to work it out
- 1
What is special about 47760: a Harshad number: divisible by its digit sum 24.
- 2
47760 is composite. Its prime factorisation is
- 3
The divisors add up to 148800; without 47760 itself that is 101040, so 47760 is abundant (101040 is more than 47760). Euler's totient φ(47760) = 12672 numbers up to 47760 share no factor with it.
- 4
The digits of 47760 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 145 steps to reach 1.
LaTeX source of the formulas on this page
\[ 47760 = 2^{4} \times 3 \times 5 \times 199 \]47760 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 148800 |
| Euler totient φ(n) | 12672 |
| Square | 2281017600 |
| Cube | 108941400576000 |
| Square root | 218.540614 (= 4√2985) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 145 |
| Scientific notation | 4.776 × |
47760 in other forms
| Form | Value |
|---|---|
| In words | forty-seven thousand seven hundred and sixty |
| Binary (base 2) | 1011101010010000 |
| Octal (base 8) | 135220 |
| Hexadecimal (base 16) | BA90 |
| Base 3 | 2102111220 |
| As time | 47760 seconds = 13 h 16 min 0 s |
Is 47760 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (47760 ÷ 2 = 23880) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (47760 ÷ 3 = 15920) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (47760 ÷ 4 = 11940) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (47760 ÷ 5 = 9552) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (47760 ÷ 6 = 7960) | 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 (47760 ÷ 8 = 5970) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (47760 ÷ 10 = 4776) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (47760 ÷ 12 = 3980) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 47760 a prime number?
No. 47760 = × 3 × 5 × 199, so it is divisible by 2.
What are the factors of 47760?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 199, 240, 398, 597, 796, 995, 1194, 1592, 1990, 2388, 2985, 3184, 3980, 4776, 5970, 7960, 9552, 11940, 15920, 23880, 47760.
What is 47760 in binary?
1011101010010000 (hexadecimal BA90, octal 135220).
What is the square root of 47760?
About 218.5406, exactly 4√2985.
Is 47760 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 47760?
47760 is a Harshad number: divisible by its digit sum 24.