Page 4 - Matematica_Mathematics - Factorul comun_Common factor

2. Common factor

In mathematics, but also in everyday life, there are methods of solving problems or situations that
greatly simplify our mission.

Suppose that there are 34,267 jars of fruit jam at a warehouse. The price of a jar is 17 lei. 28 867 jars
are delivered for sale. We need to find out what is the value of the jars of jam that remained in storage.

1st way to solve
We could calculate the value of the jars that were at first in the warehouse, then the value of the jars
that were delivered, then find out what is the value of the jam jars that were left in the warehouse.
Written in the form of an exercise, this variant of solving would be:

34 267 × 17 − 28 867 × 17 = 582 539 − 490 739 = 91 800

2nd way to solve
We will try to find a solution in which the calculations will be
simplified. We could first find out how many jars were left in storage, then
calculate their value. This time, the solution would be:

(34 267 − 28 867) × 17 = 5 400 × 17 = 91 800

Basically, by solving the problem in the two ways, you have already discovered what it means common
factor (“factorul comun”)
34 267 × 17 − 28 867 × 17 = (34 267 − 28 867) × 17

If you think about it, taken separately, the two words are familiar to you. Factors (“Factori”) are called
the numbers that multiply. So, to be a factor, the number must appear in a multiplication.

Practice

1. In which of the following examples the number 8 is factor?

The largest even number of 1 dig is 8.

8 : 4 = 2

4 + 8 = 12

8 × 4 = 32