Could one use Euclid's algorithm to find the GCD of three different numbers?

Question

I am familiar with using Euclid's algorithm for GCDs in a two-column format, like this:

integer a integer b

integer b remainder r

remainder r remainder s (of b/r)

s again remainder t (of r/s)

and so on.

Is there a mathematically sound way to adapt this to three columns to find the GCD of three integers, or am I better off using some other method?

Answer 1

Let's say we have integers a, b, and c.

Use Euclid's algorithm on a and b to find their gcd g.

Then use Euclid's algorithm on c and g to find the gcd of them.  This will be the gcd of all three numbers a,b and c.

Answer 2

You can use it first to get the gcd of the first 2 numbers. Then use it on that gcd and the third number.

Answer 3

you should find GCD of 1st and 2nd and then resultant and 3rd

other wise it is not possible in this method

for example 42,63, 105

GCD(42,63,105) = GCD(GCD(42,63), 105)

= GCD(21,105)

= 21

math kp