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# what is the greatest common factor of 1134218 and 1135620

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what is the greatest common factor of 1134218 and 1135620 77 pnxpw

Guest Nov 23, 2014

#3
+81022
+5

Heureka's method is from Euclid.....

It says that, if a - b = c  and c / b, then c / a   and c is the greatest common factor of a and b

So

1135620

- 1134218

-------------

1420

And 1420 / 1134218  →    so,  1420 / 1135620     and is the greatest common factor of both numbers......

CPhill  Nov 24, 2014
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#1
+17711
+5

Since both 1 134 218 and 1 135 620 are both even, 2 divides into both

1 134 218 ÷ 2 = 567 109

1 134 620 ÷ 2 = 567 810

After going online and finding a list of prime numbers, trying them one by one, you can get to 701:

567 109 ÷ 701 = 809

567 810 ÷ 701 = 810

Since 809 and 810 are relatively prime (no whole number divides into both of them), we can stop.

The greatest common factor is 2 x 701 = 1402.

Actually, I didn't do that. I have a calculator that, if you divide 1134218 by 1135620, you get .9987654321...

Then, by using a button that changes decimal fractions to common fractions, it gives the answer 809/810.

Dividing 1134218 by 809, the result is 1402, which is 701 x 2. Then, I went to an online list of prime numbers and finding 701, I knew that I was finished.

geno3141  Nov 23, 2014
#2
+18829
+5

what is the greatest common factor of 1134218 and 1135620

Use the euklid algorithmn:

$$a= 1135620 \ and \ b= 1134218 \ and \ a> b\\ \\ \begin{array}{c|c|c|c|c|c} \hline a & b & q & r \\ \hline 1135620 & 1134218 & \frac{a}{b}={1} & {1402} & 1135620 = {1} * 1134218 + {1402} \\ 1134218 (old\ b) & 1402(old\ r) & \frac{a}{b}={809} & {0} &1134218 = {809} * 1134218 + {0}& r= 0 \ {Stop }\\ \hline \end{array}$$

if  r = 0 then in the line before r = 1402 is the greatest common factor

heureka  Nov 24, 2014
#3
+81022
+5

Heureka's method is from Euclid.....

It says that, if a - b = c  and c / b, then c / a   and c is the greatest common factor of a and b

So

1135620

- 1134218

-------------

1420

And 1420 / 1134218  →    so,  1420 / 1135620     and is the greatest common factor of both numbers......

CPhill  Nov 24, 2014

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