Question

What is the Greatest common factor shared by 80 and 100

Answer 1

20

Explanation:

`GCD(80,100)\\\\\longrightarrow 80=2^4\cdot5\\\\\longrightarrow 100=2^2\cdot5^2\\\\`

so for two is

`2^2`

and for 5 is

`5`

so we multiply both

`\longrightarrow 2^2\cdot5 \\\\=4*5\\\\=20`

we can use the euclidean algoritm as follows

`100=80(1)+20\\\\80=20(4)\:\:\:\:\:\:\:\:\uparrow gcd`