Enter modulo statements

Using the Chinese Remainder Theorem, solve:

x ≡ 1 mod 2

x ≡ 2 mod 3

x ≡ 3 mod 4

x ≡ 4 mod 5

x ≡ 5 mod 6

Pairwise Coprime: Take the GCF of 2 and modulus

GCF(2,3) = 1

GCF(2,4) = 2

GCF(2,5) = 1

GCF(2,6) = 2

Pairwise Coprime: Take the GCF of 3 and modulus

GCF(3,4) = 1

GCF(3,5) = 1

GCF(3,6) = 3

Pairwise Coprime: Take the GCF of 4 and modulus

GCF(4,5) = 1

GCF(4,6) = 2

Pairwise Coprime: Take the GCF of 5 and modulus

GCF(5,6) = 1

Coprime check

Since at least one of our 10 GCF calculations ≠ 1

ni's are not pairwise coprime

We cannot use the regular formula for the CRT

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?

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

algorithmA process to solve a problem in a set amount of timechinese remainder theoremancient theorem that gives the conditions necessary for multiple equations to have a simultaneous integer solutioncoefficienta numerical or constant quantity placed before and multiplying the variable in an algebraic expressionequationa statement declaring two mathematical expressions are equalgcfgreatest common factor - largest positive integer dividing a set of integersmodulusthe remainder of a division, after one number is divided by another.
a mod bproductThe answer when two or more values are multiplied togetherremainderThe portion of a division operation leftover after dividing two integerssubstitutiona simple way to solve linear equations algebraically and find the solutions of the variables.theoremA statement provable using logic

Example calculations for the Chinese Remainder Theorem Calculator

Chinese Remainder Theorem Calculator Video

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