Example of Greatest Common Divisor

The greatest of the common divisors is called the Greatest Common Divisor (M.C.D.) of two or more numbers. To find the Greatest Common Divisor of several numbers, the first thing we do is decompose each of them into its prime factors. The M.C.D. is equal to the product of all common factors with their smallest exponent.
Let's study an example on the subject:
In a supermarket they pack 120 chocolate candies, 240 mint candies and 180 honey candies. How many equal bags can be packed without any candy on it? And how many candies of each taste will be included in each bag?
To begin solving this example, we find the M.C.D. of the numbers 120, 240 and 180 by breaking them down into their prime factors
No Prime factors
120 2
60 2
30 2
15 3
5 5
1
The number 120 is decomposed into its prime factors as follows, 120 = 2 x 2 x 2 x 3 x 5, 120 = 2 (cubed) x 3 x 5
No. prime factors
240 2
120 2
60 2
30 2
15 3
5 5
1
We decompose the number 240 into its prime factors like this: 240 = 2 x 2 x 2 x 2 x 3 x5, that is, 240 = 2 (raised to the fourth) x 3 x 5

No Prime factors
180 2
90 2
45 3
15 3
5 5
1
The number 180 is decomposed into its prime factors as: 180 = 2 x 2 x 3 x 3 x 5, 180 = 2 (squared) x 3 (squared) x 5
We conclude that the M.C.D. of the numbers 120, 240 and 180 = 2 (squared) x 3 x 5 or what is the same as the M.C.D. of 120, 240 and 180 = 60.
60 equal bags of candies can be packed. Each bag will have 2 chocolate candies, 4 peppermint candies, and 3 honey candies.
Remember that to decompose a number into its prime factors we must divide each number by the smallest prime number that it divides it exactly and that the Greatest Common Divisor is equal to the product of the common factors with the smallest exponent.