what is the greatest common factor of 7983 and 100000

what is the greatest common factor of 7983 and 100000

I. Euclid

$$\small{\text{ $ \begin{array}{rcrrr} & && q& r\\ 100000 & : & 7983 & 12 & 4204\\ 7983 & : & 4204& 1 & 3779\\ 4204& : & 3779& 1 & 425\\ 3779& : & 425& 8 & 379\\ 425& : & 379& 1 & 46\\ 379& : & 46& 8 & 11\\ 46& : & 11& 4 & 2\\ 11& : & 2& 5 & \textcolor[rgb]{1,0,0}{1}\\ 2& : & 1& 2 & 0 \end{array} $ }}$$

The greatest common factor of 7983 and 100000 = 1 .    They are relatively prime.

II. Prime factorization

$$\small{ \text{ $ \begin{array}{rrcrl} 100000 \quad & 2^5 &*& 5^5 & \qquad *(3^0*887^0)\\ 7983 \quad & 3^2 &*& 887^1 & \qquad *(2^0*5^0)\\ \end{array} $ }}$$

take the smallest exponents: $$2^0*3^0*5^0*887^0 = \textcolor[rgb]{1,0,0}{1}$$

1...is there only common factor

There is a neat website that factors numbers for you:

http://www.coolmathgames9.com/factors/

It says that the factors of 7983 are:  1, 3, 9, 887, 2661, and 7983.

Of these factors, the only one that is a factor of 100,000 is 1.

So, the greatest common factor of 7983 and 100,000 is 1.

How did you know that Happy?