### FPB (The greatest common divisor)

FPB

Welcome visitors..
In this post, we will explain about FPB in mathematics.

FPB stands for The greatest common divisor is an operation that processes two or more non-zero integers, the process is to find the largest integer divisor (> 1) on each number so that each number cannot be divided by a number together with a number (> 1).

There are 2 ways in the FPB process:

1. Find the factors of each number starting from the number 1 to the number itself so that the greatest common factor is obtained.
2. Converting each number to prime multiplication form, the result is by the rule: the same number written once, the same number and power is taken to the smallest power, and a different number it is not written. All the same numbers must be in every member.

Example 1:
Find FPB(4, 6) in the first way.
Solution:
Factor 4: 1, 2, 4.
Factor 6: 1, 2, 3.
So, FPB(4, 6)=2.
Example 2:
Find FPB(4, 8) in the first way.
Solution:
Factor 4: 1, 2, 4.
Factor 8: 1, 2, 4, 8.
So, FPB(4, 8)=4.

Example 3:
Find FPB(4, 6) in the second way.
Solution:
$4=(2).(2)=2^2$
$6=(2).(3)$

The same number is 2, i.e. $2^1$ and $2^2$, so we choose The smallest power is $2^1$. The different number is 3 (not included). So, FPB(4, 6)=$2^1$=2.

Example 4:
Find the FPB(36, 6, 30, 12) in the second way.
Solution:
$36=2^2.3^2$
$6=2.(3)$
$30=2.(3).(5)$
$12=(2^2).3$
So, FPB(4, 6, 15, 12)=$2.(3)$=6.

Then we will discuss examples of the use of FPB in life daily.

Example 5:

Andi has 20 oranges, 24 mangoes, and 36 apples. Andi will make the fruit package with each fruit must be present and the number of fruit is the same in each package. Define:

• How many packets of fruit can Andi produce?
• How many oranges are in one package?
• How many mangoes in one package?
• How many apples are in one package?

Solution:

This issue is about FPB. $$20=2^2.(5)$$$$24=2^3.(3)$$$$36=2^2.(3^2)$$ The same number entirely is only the number 2, which we choose the power of the smallest is $2^2$. So the FPB is 4. So, lots of fruit packages What Andi can make is 4 packages. In one package each lot of fruit oranges, mangoes, and apples are: 20/4, 24/4, and 36/4 or 5, 6, and 9 fruits.