The number 5712
5712 is a composite number with 40 divisors. Its prime factorisation is × 3 × 7 × 17. Divisors (40): 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 17, 21, 24, 28, 34, 42 … 5712.
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How to work it out
- 1
What is special about 5712: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
5712 is composite. Its prime factorisation is
- 3
The divisors add up to 17856; without 5712 itself that is 12144, so 5712 is abundant (12144 is more than 5712). Euler's totient φ(5712) = 1536 numbers up to 5712 share no factor with it.
- 4
The digits of 5712 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 36 steps to reach 1.
LaTeX source of the formulas on this page
\[ 5712 = 2^{4} \times 3 \times 7 \times 17 \]5712 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 17856 |
| Euler totient φ(n) | 1536 |
| Square | 32626944 |
| Cube | 186365104128 |
| Square root | 75.577775 (= 4√357) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 36 |
| Scientific notation | 5.712 × |
5712 in other forms
| Form | Value |
|---|---|
| In words | five thousand seven hundred and twelve |
| Binary (base 2) | 1011001010000 |
| Octal (base 8) | 13120 |
| Hexadecimal (base 16) | 1650 |
| Base 3 | 21211120 |
| As time | 5712 seconds = 1 h 35 min 12 s |
Is 5712 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (5712 ÷ 2 = 2856) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (5712 ÷ 3 = 1904) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (5712 ÷ 4 = 1428) | 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 (5712 ÷ 6 = 952) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (5712 ÷ 7 = 816) | 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 (5712 ÷ 8 = 714) | 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 | No (remainder 2) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (5712 ÷ 12 = 476) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 5712 a prime number?
No. 5712 = × 3 × 7 × 17, so it is divisible by 2.
What are the factors of 5712?
1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 17, 21, 24, 28, 34, 42, 48, 51, 56, 68, 84, 102, 112, 119, 136, 168, 204, 238, 272, 336, 357, 408, 476, 714, 816, 952, 1428, 1904, 2856, 5712.
What is 5712 in binary?
1011001010000 (hexadecimal 1650, octal 13120).
What is the square root of 5712?
About 75.5778, exactly 4√357.
Is 5712 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 5712?
5712 is a happy number: repeatedly adding the squares of its digits reaches 1.