Nitpick: there’s no way to apply the Chinese Remainder Theorem. It merely states that “if one knows the remainders of the Euclidean division of an integer n by several integers, then one can* determine uniquely the remainder of the division of n by the product of these integers, under the condition that the divisors are pairwise coprime.”* (https://en.wikipedia.org/wiki/Chinese_remainder_theorem) It doesn’t say how to determine that number.

https://en.wikipedia.org/wiki/Chinese_remainder_theorem#Comp... describes a few algorithms for doing that.