### 2,700 and 15 are not coprime (relatively, mutually prime) if they have common prime factors, that is, if their greatest (highest) common factor (divisor), gcf, hcf, gcd, is not 1.

## Calculate the greatest (highest) common factor (divisor), gcf, hcf, gcd

### Approach 1. Integer numbers divisibility:

#### Divide the larger number by the smaller one.

#### Notice that dividing our numbers leaves no remainder:

#### 2,700 ÷ 15 = 180 + 0;

#### So, 2,700 = 15 × 180;

#### So, 2,700 is divisible by 15;

#### 15 is a factor (a divisor) of 2,700;

#### Consequently, gcf, hcf, gcd (15; 2,700) = 15.

## Coprime numbers (relatively prime) (15; 2,700)? No.

gcf, hcf, gcd (15; 2,700) = 15.

### Approach 2. Integer numbers prime factorization:

#### Prime Factorization of a number: finding the prime numbers that multiply together to make that number.

#### 2,700 = 2^{2} × 3^{3} × 5^{2};

2,700 is not a prime, is a composite number;

#### 15 = 3 × 5;

15 is not a prime, is a composite number;

#### Positive integers that are only dividing by themselves and 1 are called prime numbers. A prime number has only two factors: 1 and itself.

#### A composite number is a positive integer that has at least one factor (divisor) other than 1 and itself.

### Calculate greatest (highest) common factor (divisor):

#### Multiply all the common prime factors, by the lowest exponents (if any).

#### gcf, hcf, gcd (2,700; 15) = 3 × 5 = 15;

## Coprime numbers (relatively prime) (2,700; 15)? No.

2,700 has all the prime factors of the number 15.

gcf, hcf, gcd (15; 2,700) = 15.