The number 47872
47872 is a composite number with 36 divisors. Its prime factorisation is × 11 × 17. Divisors (36): 1, 2, 4, 8, 11, 16, 17, 22, 32, 34, 44, 64, 68, 88, 128, 136 … 47872.
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How to work it out
- 1
47872 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
47872 is composite. Its prime factorisation is
- 3
The divisors add up to 110376; without 47872 itself that is 62504, so 47872 is abundant (62504 is more than 47872). Euler's totient φ(47872) = 20480 numbers up to 47872 share no factor with it.
- 4
The digits of 47872 add up to 28, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 52 steps to reach 1.
LaTeX source of the formulas on this page
\[ 47872 = 2^{8} \times 11 \times 17 \]47872 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 110376 |
| Euler totient φ(n) | 20480 |
| Square | 2291728384 |
| Cube | 109709621198848 |
| Square root | 218.796709 (= 16√187) |
| Digit sum / digital root | 28 / 1 |
| Collatz steps to 1 | 52 |
| Scientific notation | 4.7872 × |
47872 in other forms
| Form | Value |
|---|---|
| In words | forty-seven thousand eight hundred and seventy-two |
| Binary (base 2) | 1011101100000000 |
| Octal (base 8) | 135400 |
| Hexadecimal (base 16) | BB00 |
| Base 3 | 2102200001 |
| As time | 47872 seconds = 13 h 17 min 52 s |
Is 47872 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (47872 ÷ 2 = 23936) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (47872 ÷ 4 = 11968) | 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 | No (remainder 4) | 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 (47872 ÷ 8 = 5984) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 1) | 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 | Yes (47872 ÷ 11 = 4352) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 47872 a prime number?
No. 47872 = × 11 × 17, so it is divisible by 2.
What are the factors of 47872?
1, 2, 4, 8, 11, 16, 17, 22, 32, 34, 44, 64, 68, 88, 128, 136, 176, 187, 256, 272, 352, 374, 544, 704, 748, 1088, 1408, 1496, 2176, 2816, 2992, 4352, 5984, 11968, 23936, 47872.
What is 47872 in binary?
1011101100000000 (hexadecimal BB00, octal 135400).
What is the square root of 47872?
About 218.7967, exactly 16√187.
Is 47872 divisible by 3?
No. Its digits add up to 28, which is not a multiple of 3.
What is special about the number 47872?
It is a composite number with 36 divisors.