Infinite fractions \[ \text{When is }\ x \mid y \text{ ?} \ \] x can be represent as \[ {x} = \prod_{i=1}^n p_{i}^{k} \] \[ \text{where}\ p_{i} =\text{ is a prime factor of } {x} \text{ and } {x} \text{ has } {n} \text{ prime factors.} \] \[ \text{Example: }\ {x} = {12} = {2}^{2} \times {3} \] We can represent the y by the same way. x divides y ( x is a divisor of y ) if and only if all prime factors of x are available in y prime factorization and each prime factor (p) power (p^a) in x factorization is less than equal to prime factor (p) power (p^b) in y factorization (a <= b). Or we can say that when GCD(x, y) = x , x divides y. \[ \text{When is }\ x\nmid y \text{ ?} \ \] y = q * x + r [ where r < x ] When reminder (r) is not equal to 0, y is not divisible by x. Only when r is not equal to zero there are numbers after the decimal point of fraction p/q. How to get numbers after the decimal point of a fraction ? We recursively do it until MOD = 0. init...
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