### 14 and 27 are coprime (relatively prime)... if:

#### If there is no number other than 1 that evenly divides (without a remainder) both numbers. Or...

#### Or, in other words, if their greatest (highest) common factor (divisor), gcf (hcf, gcd), is equal to 1.

## Calculate the greatest (highest) common factor (divisor),

gcf (hcf, gcd), of the two numbers

### Method 1. The prime factorization:

#### The prime factorization of a number: finding the prime numbers that multiply together to make that number.

#### 14 = 2 × 7

14 is not a prime number, is a composite one.

#### 27 = 3^{3}

27 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).

#### Step 1. Divide the larger number by the smaller one:

27 ÷ 14 = 1 + 13

Step 2. Divide the smaller number by the above operation's remainder:

14 ÷ 13 = 1 + 1

Step 3. Divide the remainder of the step 1 by the remainder of the step 2:

13 ÷ 1 = 13 + 0

At this step, the remainder is zero, so we stop:

1 is the number we were looking for - the last non-zero remainder.

This is the greatest (highest) common factor (divisor).

### gcf (hcf, gcd) (14; 27) = 1

## Coprime numbers (prime to each other, relatively prime) (14; 27)? Yes.

gcf (hcf, gcd) (14; 27) = 1