#7**+30 **

**I do not get what you have done Heureka**

\(\begin{array}{rcll} 210 & \color{blue}+++ & \color{blue}+++& \color{blue}+++ &\color{blue} +++ &\color{blue}+++ &\color{blue}+++ &\color{blue}+++ \\ -90 & \color{green}+++ & \color{green}+++& \color{green}+++ \\ = 120 & &&& \color{blue} +++ &\color{blue}+++ &\color{blue}+++ &\color{blue}+++ \\ \hline 120 & \color{blue} +++ &\color{blue}+++ &\color{blue}+++ &\color{blue}+++ \\ -90 & \color{green}+++ & \color{green}+++& \color{green}+++ \\ = 30 & &&& \color{blue} +++\\ \hline 90 & \color{green}+++ & \color{green}+++& \color{green}+++ \\ - 30 & \color{blue} +++\\ =60 & & \color{green}+++ & \color{green}+++ \\ \hline 60 & \color{green}+++ & \color{green}+++ \\ -30 & \color{blue} +++\\ 30 & & \color{green}+++\\ \hline 30 & \color{blue}+++\\ =30 & \color{green}+++\\ \end{array}\\ \begin{array}{rcl} \text{gcd}(210,90) = 30, \text{ because blue and green are equal} \end{array}\\\)

heureka
Dec 3, 2015

#1**+20 **

**Find the greatest common factor of 210 and 90 **

\(\begin{array}{rcl} 210 - 90 &=& 120 \\ 120 - 90 &=& 30 \\ 90 - 30 &=& 60 \\ 60 - \mathbf{30} &=& \mathbf{30} \end{array}\\\)

The greatest common factor of 210 and 90 is** 30**

heureka
Dec 3, 2015

#2**+10 **

BrainFreeze,

Are you even looking at the answers that you have already been given?

You have been logged on for hours but you have not responded to any of the answerers who have already tried to help you.

Maybe you can be more polite this time and show an interest in the answer that Heureka has prepared especially for you.

Melody
Dec 3, 2015

#5**+10 **

ok no worries,

Do not forget to thank heureka :)

It is best to do it on the forum so everyone can see your good manners :)

Melody
Dec 3, 2015

#7**+30 **

Best Answer

**I do not get what you have done Heureka**

\(\begin{array}{rcll} 210 & \color{blue}+++ & \color{blue}+++& \color{blue}+++ &\color{blue} +++ &\color{blue}+++ &\color{blue}+++ &\color{blue}+++ \\ -90 & \color{green}+++ & \color{green}+++& \color{green}+++ \\ = 120 & &&& \color{blue} +++ &\color{blue}+++ &\color{blue}+++ &\color{blue}+++ \\ \hline 120 & \color{blue} +++ &\color{blue}+++ &\color{blue}+++ &\color{blue}+++ \\ -90 & \color{green}+++ & \color{green}+++& \color{green}+++ \\ = 30 & &&& \color{blue} +++\\ \hline 90 & \color{green}+++ & \color{green}+++& \color{green}+++ \\ - 30 & \color{blue} +++\\ =60 & & \color{green}+++ & \color{green}+++ \\ \hline 60 & \color{green}+++ & \color{green}+++ \\ -30 & \color{blue} +++\\ 30 & & \color{green}+++\\ \hline 30 & \color{blue}+++\\ =30 & \color{green}+++\\ \end{array}\\ \begin{array}{rcl} \text{gcd}(210,90) = 30, \text{ because blue and green are equal} \end{array}\\\)

heureka
Dec 3, 2015

#8**+5 **

**Thanks Heureka,**

I understand but it is still really weird. I will muck around with it some more.

I would just have broken them into their prime factors.

I suppose your way is quicker.... I will have to think about it. ........

My way

90=10*9=2*5*3*3

210=10*21=2*5*3*7

so GCF=2*5*3 =30

Melody
Dec 3, 2015