The number 47712
47712 is a composite number with 48 divisors. Its prime factorisation is × 3 × 7 × 71. Divisors (48): 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48 … 47712.
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How to work it out
- 1
What is special about 47712: a Harshad number: divisible by its digit sum 21.
- 2
47712 is composite. Its prime factorisation is
- 3
The divisors add up to 145152; without 47712 itself that is 97440, so 47712 is abundant (97440 is more than 47712). Euler's totient φ(47712) = 13440 numbers up to 47712 share no factor with it.
- 4
The digits of 47712 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 96 steps to reach 1.
LaTeX source of the formulas on this page
\[ 47712 = 2^{5} \times 3 \times 7 \times 71 \]47712 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 145152 |
| Euler totient φ(n) | 13440 |
| Square | 2276434944 |
| Cube | 108613264048128 |
| Square root | 218.430767 (= 4√2982) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 96 |
| Scientific notation | 4.7712 × |
47712 in other forms
| Form | Value |
|---|---|
| In words | forty-seven thousand seven hundred and twelve |
| Binary (base 2) | 1011101001100000 |
| Octal (base 8) | 135140 |
| Hexadecimal (base 16) | BA60 |
| Base 3 | 2102110010 |
| As time | 47712 seconds = 13 h 15 min 12 s |
Is 47712 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (47712 ÷ 2 = 23856) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (47712 ÷ 3 = 15904) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (47712 ÷ 4 = 11928) | 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 (47712 ÷ 6 = 7952) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (47712 ÷ 7 = 6816) | 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 (47712 ÷ 8 = 5964) | 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 | No (remainder 2) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (47712 ÷ 12 = 3976) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 47712 a prime number?
No. 47712 = × 3 × 7 × 71, so it is divisible by 2.
What are the factors of 47712?
1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 71, 84, 96, 112, 142, 168, 213, 224, 284, 336, 426, 497, 568, 672, 852, 994, 1136, 1491, 1704, 1988, 2272, 2982, 3408, 3976, 5964, 6816, 7952, 11928, 15904, 23856, 47712.
What is 47712 in binary?
1011101001100000 (hexadecimal BA60, octal 135140).
What is the square root of 47712?
About 218.4308, exactly 4√2982.
Is 47712 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 47712?
47712 is a Harshad number: divisible by its digit sum 21.