The factors of 12 are 1,2,3,4,6, and 12. On the other hand, the factors of 18 are 1,2,3,6,9, and 18. The factors of 12 and 18 are the numbers that evenly divide them without leaving a remainder.

The common factors between the factors of both 12 and 18 are: 1, 2, 3, and 6, as shown below:

Therefore, the Greatest Common Divisor (GCD) of both 12 and 18 is **6**.

The GCD is also referred to as the *Greatest Common Factor (GCF)*, or the *Highest Common Factor*. Therefore, in Math questions, you can be asked to find the GCD, the GCF, or the HCF. All these terms refer to the same thing discussed here, and the approach of solving them is them same for all.

In our example above, we have used the first option as:

12: 1,2,3,4,6, and 12.

18: 1,2,3,6,9, and 18.

The common factors are 1, 2, 3, and 6. Hence, the GCD is**6**.

12: 1,2,3,4,6, and 12.

18: 1,2,3,6,9, and 18.

The common factors are 1, 2, 3, and 6. Hence, the GCD is

Alternatively, we can do as follows:

Then we get the product of the common factors; 2 and 3 (2 × 3 = 6). Hence the GCD by*option 2* is 6.

Then we get the product of the common factors; 2 and 3 (2 × 3 = 6). Hence the GCD by

Find the GCD of 73, 96, 300

**Solution**

Then we get the product of the common factors; 2^{2} and 3 (2 × 2 × 3 = 12). Hence the GCD by *option 2* is 12. Try solving it using the first option. Hint: You should still get 12 as your GCD.

Then we get the product of the common factors; 2

Find the greatest number which, when divided by 181 and 236, leaves a remainder of 5 in each case.

**Solution**

First, we subtract 5 from each number to give:

181 - 5 = 176

236 - 5 = 231

Lets find the GCD of 176 and 231

The common factor of both 176 and 231 is 11.

First, we subtract 5 from each number to give:

181 - 5 = 176

236 - 5 = 231

Lets find the GCD of 176 and 231

The common factor of both 176 and 231 is 11.

Three similar iron bars of length 200cm, 300 cm, and 360 cm are cut into equal pieces. Find the largest possible area of a square which can be made from any of the three pieces.

**Solution**

First, we get the GCD.

Then we get the product of the common factors; 2^{2} and 5 (2 × 2 × 5 = 20). Therefore, the largest common length of the 3 bars is 20cm.

Area of a square is L × L; where L = 20;

Area = 20 × 20 = 400cm^{2}

First, we get the GCD.

Then we get the product of the common factors; 2

Area of a square is L × L; where L = 20;

Area = 20 × 20 = 400cm

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