### 5,746 and 3,240 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 prime factorization:

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

#### 5,746 = 2 × 13^{2} × 17

5,746 is not a prime number, is a composite one.

#### 3,240 = 2^{3} × 3^{4} × 5

3,240 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:

5,746 ÷ 3,240 = 1 + 2,506

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

3,240 ÷ 2,506 = 1 + 734

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

2,506 ÷ 734 = 3 + 304

Step 4. Divide the remainder of the step 2 by the remainder of the step 3:

734 ÷ 304 = 2 + 126

Step 5. Divide the remainder of the step 3 by the remainder of the step 4:

304 ÷ 126 = 2 + 52

Step 6. Divide the remainder of the step 4 by the remainder of the step 5:

126 ÷ 52 = 2 + 22

Step 7. Divide the remainder of the step 5 by the remainder of the step 6:

52 ÷ 22 = 2 + 8

Step 8. Divide the remainder of the step 6 by the remainder of the step 7:

22 ÷ 8 = 2 + 6

Step 9. Divide the remainder of the step 7 by the remainder of the step 8:

8 ÷ 6 = 1 + 2

Step 10. Divide the remainder of the step 8 by the remainder of the step 9:

6 ÷ 2 = 3 + 0

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

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

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

### gcf (hcf, gcd) (5,746; 3,240) = 2 ≠ 1

## Coprime numbers (prime to each other, relatively prime) (5,746; 3,240)? No.

gcf (hcf, gcd) (3,240; 5,746) = 2 ≠ 1