 # Chinese Remainder Theorem Calculator

## Enter Chinese Remainder Statements

### How does the Chinese Remainder Theorem Calculator work?

Free Chinese Remainder Theorem Calculator - Given a set of modulo equations in the form:
x ≡ a mod b
x ≡ c mod d
x ≡ e mod f

the calculator will use the Chinese Remainder Theorem to find the lowest possible solution for x in each modulus equation.
Given that the ni portions are not pairwise coprime and you entered two modulo equations, then the calculator will attempt to solve using the Method of Successive Subsitution
This calculator has 1 input.

### What 1 formula is used for the Chinese Remainder Theorem Calculator?

c = N/n

For more math formulas, check out our Formula Dossier

### What 10 concepts are covered in the Chinese Remainder Theorem Calculator?

algorithm
A process to solve a problem in a set amount of time
chinese remainder theorem
ancient theorem that gives the conditions necessary for multiple equations to have a simultaneous integer solution
coefficient
a numerical or constant quantity placed before and multiplying the variable in an algebraic expression
equation
a statement declaring two mathematical expressions are equal
gcf
greatest common factor - largest positive integer dividing a set of integers
modulus
the remainder of a division, after one number is divided by another.
a mod b
product
The answer when two or more values are multiplied together
remainder
The portion of a division operation leftover after dividing two integers
substitution
a simple way to solve linear equations algebraically and find the solutions of the variables.
theorem
A statement provable using logic