### 1,572 and 12 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:

#### 1,572 ÷ 12 = 131 + 0

#### ⇒ 1,572 = 12 × 131

#### ⇒ 1,572 is divisible by 12

#### ⇒ 12 is a factor (a divisor) of 1,572

### Consequently, gcf (hcf, gcd) (12; 1,572) = 12 ≠ 1

## Coprime numbers (prime to each other, relatively prime) (12; 1,572)? No.

gcf (hcf, gcd) (12; 1,572) = 12 ≠ 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.

#### 1,572 = 2^{2} × 3 × 131

1,572 is not a prime number, is a composite one.

#### 12 = 2^{2} × 3

12 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).