The definition that controls Coprime
Two integers are coprime precisely when their greatest common divisor is one. Neither number must itself be prime.
Math calculator
Coprime Checker
Check whether two integers share no positive factor greater than one. The calculation trail makes the reported coprime result easier to reproduce.
Coprime Checker inputs
Values for this result
What a Coprime result can support
Reduced fractions, modular inverses, Euler’s theorem, and repeating cycles often require coprime inputs.
When the Coprime shortcut is insufficient
The pair 1 and any integer is coprime. The pair 0 and ±1 is coprime, but zero with any other magnitude is not.
Working through Coprime on paper
Apply the Euclidean algorithm to the absolute values. A final nonzero divisor of one means the pair is coprime.
Thirty-five and sixty-four have GCF one, so they are coprime even though 35 is composite. This Coprime Checker example can be compared with greatest common factor.
Testing Coprime beyond the example
Keep First integer integral when Coprime requires integers. Verify Second integer through the defining Coprime identity.
Test zero in Coprime, then test one in Coprime. Rebuild the starting integer through Coprime.
Before carrying Coprime result into another step, test Coprime with a nearby round value for First integer. Retaining Second integer makes the comparison interpretable and helps separate a numerical surprise from a setup error.
Before accepting Coprime result, restore the Coprime inputs First integer and Second integer. Estimate Coprime result independently. Then vary Second integer alone and observe the new Coprime output. This isolates the changed part of Coprime.
Reverse the Coprime reasoning once: begin with the shown Coprime result and ask whether First integer could produce it under Second integer. When that Coprime relationship fails, the contradiction narrows the error to an entry, order choice, or convention.
Cross-checking Coprime
Keep extra digits in Coprime result until the next step is known. Early rounding can obscure whether First integer and Second integer satisfy the Coprime relation. Round the final Coprime result once, using precision appropriate to the original Coprime data.
Validating Coprime
Vary First integer alone to test Coprime sensitivity. Freeze Second integer and watch Coprime result. Several simultaneous edits would hide which part of the Coprime setup caused the change in Coprime result.
Questions about Coprime
Must both numbers be prime?
No.
Are consecutive integers coprime?
Yes.
Is 1 coprime with every integer?
Yes.
Can two even numbers be coprime?
No, because both share factor 2.