### 16 and 46,288 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:

#### 46,288 ÷ 16 = 2,893 + 0;

#### So, 46,288 = 16 × 2,893;

#### So, 46,288 is divisible by 16;

#### 16 is a factor (a divisor) of 46,288;

#### Consequently, gcf, hcf, gcd (16; 46,288) = 16.

## Coprime numbers (relatively prime) (16; 46,288)? No.

gcf, hcf, gcd (16; 46,288) = 16.

### Approach 2. Integer numbers prime factorization:

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

#### 16 = 2^{4};

16 is not a prime, is a composite number;

#### 46,288 = 2^{4} × 11 × 263;

46,288 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 (16; 46,288) = 2^{4} = 16;

## Coprime numbers (relatively prime) (16; 46,288)? No.

46,288 has all the prime factors of the number 16.

gcf, hcf, gcd (16; 46,288) = 16.