Checking for co-prime numbers - JavaScript

Two numbers are said to be co-primes if there exists no common prime factor amongst them (1 is not a prime number).

For example:

4 and 5 are co-primes
9 and 14 are co-primes
18 and 35 are co-primes
21 and 57 are not co-prime because they have 3 as the common prime factor

We are required to write a function that takes in two numbers and returns true if they are co-primes otherwise returns false.

Understanding Co-prime Numbers

Two numbers are co-prime if their greatest common divisor (GCD) is 1. This means they share no common factors other than 1.

Method 1: Using Loop to Check Common Factors

This approach iterates through all possible divisors and checks if both numbers share any common factor:

const areCoprimes = (num1, num2) => {
    const smaller = num1 > num2 ? num2 : num1;
    for(let ind = 2; ind <= smaller; ind++){
        const condition1 = num1 % ind === 0;
        const condition2 = num2 % ind === 0;
        if(condition1 && condition2){
            return false;
        }
    }
    return true;
};

console.log(areCoprimes(4, 5));
console.log(areCoprimes(9, 14));
console.log(areCoprimes(18, 35));
console.log(areCoprimes(21, 57));

true
true
true
false

Method 2: Using GCD (More Efficient)

A more efficient approach uses the Euclidean algorithm to find the GCD. If GCD equals 1, the numbers are co-prime:

const gcd = (a, b) => {
    return b === 0 ? a : gcd(b, a % b);
};

const areCoprimes = (num1, num2) => {
    return gcd(Math.abs(num1), Math.abs(num2)) === 1;
};

console.log(areCoprimes(4, 5));   // true
console.log(areCoprimes(9, 14));  // true
console.log(areCoprimes(18, 35)); // true
console.log(areCoprimes(21, 57)); // false
console.log(areCoprimes(15, 25)); // false (GCD = 5)

true
true
true
false
false

Comparison

Conclusion

The GCD method is more efficient for large numbers, while the loop method is simpler to understand. Both approaches correctly identify co-prime numbers by checking for common factors.