The number 67712
67712 is a composite number with 24 divisors. Its prime factorisation is × . Divisors (24): 1, 2, 4, 8, 16, 23, 32, 46, 64, 92, 128, 184, 368, 529, 736, 1058 … 67712.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 67712: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 23.
- 2
67712 is composite. Its prime factorisation is
- 3
The divisors add up to 141015; without 67712 itself that is 73303, so 67712 is abundant (73303 is more than 67712). Euler's totient φ(67712) = 32384 numbers up to 67712 share no factor with it.
- 4
The digits of 67712 add up to 23, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 37 steps to reach 1.
LaTeX source of the formulas on this page
\[ 67712 = 2^{7} \times 23^{2} \]67712 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 141015 |
| Euler totient φ(n) | 32384 |
| Square | 4584914944 |
| Cube | 310453760688128 |
| Square root | 260.215295 (= 184√2) |
| Digit sum / digital root | 23 / 5 |
| Collatz steps to 1 | 37 |
| Scientific notation | 6.7712 × |
67712 in other forms
| Form | Value |
|---|---|
| In words | sixty-seven thousand seven hundred and twelve |
| Binary (base 2) | 10000100010000000 |
| Octal (base 8) | 204200 |
| Hexadecimal (base 16) | 10880 |
| Base 3 | 10102212212 |
| As time | 67712 seconds = 18 h 48 min 32 s |
Is 67712 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (67712 ÷ 2 = 33856) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (67712 ÷ 4 = 16928) | 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 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 (67712 ÷ 8 = 8464) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 5) | 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 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 67712 a prime number?
No. 67712 = × , so it is divisible by 2.
What are the factors of 67712?
1, 2, 4, 8, 16, 23, 32, 46, 64, 92, 128, 184, 368, 529, 736, 1058, 1472, 2116, 2944, 4232, 8464, 16928, 33856, 67712.
What is 67712 in binary?
10000100010000000 (hexadecimal 10880, octal 204200).
What is the square root of 67712?
About 260.2153, exactly 184√2.
Is 67712 divisible by 3?
No. Its digits add up to 23, which is not a multiple of 3.
What is special about the number 67712?
67712 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 23.