# How to find the greatest common divisor of two whole numbers How to find the greatest common divisor of two whole numbers

The greatest common divisor (GCF) of two whole numbers is the largest whole number that is a divisor (factor) of both. For example, the longest number dividing 20 and 16 is 4. In school, the “guess and check” method is commonly taught. Instead, this is a simple and systematic way to do this and always find the correct answer. This method is called "Euclid's algorithm". Let's call the two numbers "a" and "b".

## Steps

### Method 1 of 2: Use the Divider Algorithm

#### Step 2. Learn your vocabulary:

when you divide 32 by 5,

• 32 is the dividend
• 5 is the divisor
• 6 is the quotient
• 2 is the remainder.

#### Step 3. Identify the larger number of the two

That will be the dividend, and the smaller the divisor.

#### Step 4. Write this algorithm:

(dividend) = (divisor) * (quotient) + (remainder)

#### Step 12. Notice how 30 and 18 change position on the second line

Then 18 and 12 on the third line, and 12 and 6 on the fourth line. The 3, 1, 1, and 2 that follow after the multiplication symbol do not reappear. They represent how many times the divisor fits in the dividend, so they are unique on each line.

### Method 2 of 2: Use Prime Factors

#### Step 2. Find the prime factors of the numbers, and list them as shown below

• Using 24 and 18 as an example:

• 24- 2 x 2 x 2 x 3
• 18- 2 x 3 x 3
• Using 50 and 35 as an example:

• 50- 2 x 5 x 5
• 35- 5 x 7

#### Step 3. Identify all the common prime factors

• Using 24 and 18 as an example:

• 24-

Step 2. x 2 x 2

Step 3.

• 18-

#### Step 2

Step 3. x 3

• Using 50 and 35 as an example:

• 50- 2 x

Step 5. x 5

• 35-

Step 5. x 7

#### Step 4. Multiply the common factors together

• In the case of 24 and 18, multiply the

#### Step 2

Step 3. to get

Step 6.. The 6 is the greatest common factor of 24 and 18.

• In the case of 50 and 35, there is nothing to multiply.

Step 5. it is the only common factor, and therefore it is the largest.