In number theory, two positive integers are said to be coprime (or co-prime) if their greatest common divisor (GCD) is 1. In other words, they have no common factors other than 1.

For example, 4 and 9 are coprime because the factors of 4 are 1, 2, and 4, and the factors of 9 are 1, 3, and 9. The only factor that they have in common is 1, so their GCD is 1, making them coprime.

On the other hand, 8 and 12 are not coprime because the factors of 8 are 1, 2, 4, and 8, while the factors of 12 are 1, 2, 3, 4, 6, and 12. The common factors of 8 and 12 are 1, 2, and 4, so their GCD is 4, and they are not coprime.

Another example is 21 and 25. The factors of 21 are 1, 3, 7, and 21, while the factors of 25 are 1, 5, and 25. The only factor that they have in common is 1, so their GCD is 1, and they are coprime.

Coprime numbers are important in various branches of mathematics, including number theory, cryptography, and computer science. They also have practical applications in areas such as signal processing and error-correcting codes.

References : What is co prime number?