The number 47772
47772 is a composite number with 18 divisors. Its prime factorisation is × × 1327. Divisors (18): 1, 2, 3, 4, 6, 9, 12, 18, 36, 1327, 2654, 3981, 5308, 7962, 11943, 15924 … 47772.
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How to work it out
- 1
What is special about 47772: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
47772 is composite. Its prime factorisation is
- 3
The divisors add up to 120848; without 47772 itself that is 73076, so 47772 is abundant (73076 is more than 47772). Euler's totient φ(47772) = 15912 numbers up to 47772 share no factor with it.
- 4
The digits of 47772 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 101 steps to reach 1.
LaTeX source of the formulas on this page
\[ 47772 = 2^{2} \times 3^{2} \times 1327 \]47772 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 18 |
| Sum of divisors | 120848 |
| Euler totient φ(n) | 15912 |
| Square | 2282163984 |
| Cube | 109023537843648 |
| Square root | 218.568067 (= 6√1327) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 101 |
| Scientific notation | 4.7772 × |
47772 in other forms
| Form | Value |
|---|---|
| In words | forty-seven thousand seven hundred and seventy-two |
| Binary (base 2) | 1011101010011100 |
| Octal (base 8) | 135234 |
| Hexadecimal (base 16) | BA9C |
| Base 3 | 2102112100 |
| As time | 47772 seconds = 13 h 16 min 12 s |
Is 47772 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (47772 ÷ 2 = 23886) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (47772 ÷ 3 = 15924) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (47772 ÷ 4 = 11943) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (47772 ÷ 6 = 7962) | 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 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (47772 ÷ 9 = 5308) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 2) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (47772 ÷ 12 = 3981) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 47772 a prime number?
No. 47772 = × × 1327, so it is divisible by 2.
What are the factors of 47772?
1, 2, 3, 4, 6, 9, 12, 18, 36, 1327, 2654, 3981, 5308, 7962, 11943, 15924, 23886, 47772.
What is 47772 in binary?
1011101010011100 (hexadecimal BA9C, octal 135234).
What is the square root of 47772?
About 218.5681, exactly 6√1327.
Is 47772 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 47772?
47772 is a happy number: repeatedly adding the squares of its digits reaches 1.