2 and 18 are not relatively prime... if:
If there is at least one number other than 1 that evenly divides the two numbers (without a remainder). Or...
Or, in other words, if their greatest (highest) common factor (divisor), gcf (hcf, gcd), is not equal to 1.
Calculate the greatest (highest) common factor (divisor),
gcf (hcf, gcd), of the two numbers
Method 1. The divisibility of numbers:
Divide the larger number by the smaller one.
When dividing the two numbers, there is no remainder:
18 ÷ 2 = 9 + 0
⇒ 18 = 2 × 9
⇒ 18 is divisible by 2
⇒ 2 is a factor (a divisor) of 18
Consequently, gcf (hcf, gcd) (2; 18) = 2 ≠ 1
Coprime numbers (prime to each other, relatively prime) (2; 18)? No.
gcf (hcf, gcd) (2; 18) = 2 ≠ 1
Scroll down for the 2nd method...
Method 2. The prime factorization:
The prime factorization of a number: finding the prime numbers that multiply together to make that number.
2 is a prime number, it cannot be prime factorized.
18 = 2 × 32
18 is not a prime number, is a composite one.
Prime number: a number that is divisible (dividing evenly) only by 1 and itself. A prime number has only two factors: 1 and itself.
Composite number: a natural number that has at least one other factor than 1 and itself.
Calculate the greatest (highest) common factor (divisor), gcf (hcf, gcd):
Multiply all the common prime factors of the two numbers, taken by their smallest exponents (powers).