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

Two methods used below.

### Approach 1. Integer numbers divisibility:

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

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

#### 6,599,669,076 ÷ 68,796 = 95,931 + 0;

#### So, 6,599,669,076 = 68,796 × 95,931;

#### So, 6,599,669,076 is divisible by 68,796;

#### 68,796 is a factor (a divisor) of 6,599,669,076;

#### Consequently, gcf, hcf, gcd (68,796; 6,599,669,076) = 68,796.

#### Note that this is also the first step of the Euclidean Algorithm, where the division of the numbers stops when a remainder equal to zero is reported.

## Coprime numbers (relatively prime) (68,796; 6,599,669,076)? No.

gcf, hcf, gcd (68,796; 6,599,669,076) = 68,796.

### Approach 2. Integer numbers prime factorization:

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

#### 68,796 = 2^{2} × 3^{3} × 7^{2} × 13;

68,796 is not a prime, is a composite number;

#### 6,599,669,076 = 2^{2} × 3^{6} × 7^{2} × 11 × 13 × 17 × 19;

6,599,669,076 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 (68,796; 6,599,669,076) = 2^{2} × 3^{3} × 7^{2} × 13 = 68,796;

## Coprime numbers (relatively prime) (68,796; 6,599,669,076)? No.

6,599,669,076 has all the prime factors of the number 68,796.

gcf, hcf, gcd (68,796; 6,599,669,076) = 68,796.