We can write numbers as a product (multiplication) of prime numbers. However, what is the purpose of factoring these numbers? Do I need to do the factorization separately or can I do it simultaneously with two or more numbers? These issues will be discussed in our text.
One of the important points of factorization is found in the calculation of the M.D.C (Maximum Common Divisor) and the M.M.C (Least Common Multiple). However, we must be careful about obtaining these values, as we will use the same factorization procedure, that is, the same factorization of two or more numbers gives us the value of M.D.C and M.M.C. Therefore, we must understand and differentiate the way in which each of these values is obtained, through factoring simultaneous.
Let's look at an example in which simultaneous factoring was done:
Note that in the factorization, the numbers that simultaneously divided the numbers 12 and 42 were highlighted. This is an important step to be able to determine the M.D.C. If we were to list the divisors of each of the numbers, we would have the following situation:
D(12)={2,3,4,6,12}
D(42)={2,3,6,7,21,42}
Note that the largest of the common divisors between the numbers 12 and 42 is the number 6. Observing our simultaneous factorization, this value 6 is obtained by multiplying the common divisors.
On the other hand, the M.M.C will be obtained in a different way. As these are multiples, we must multiply all the factorization divisors. Thus, the M.M.C (12.14) = 2x2x3x7=84.
By Gabriel Alessandro de Oliveira
Graduated in Mathematics
Kids School Team
