Question

Calculate (228, 432, 320) in two ways: using Euclidean algorithm, and by factorization.

Answer 1

4

Explanation:

gcf(432,320,228)=gcf(gcf(432,320),228)

432=320(1)+112

320=112(2)+96

112=96(1)+16

96=16(6)

So the gcf(432,320)=16.

So now we need to find gcf(16,228)

228=16(14)+4

16=4(4)

Therefore,

gcf(432,320, 228)

=gcf(gcf(432,320),228)

=gcf(16, 228)=4

===================================

432=4(108)=4(2)(54)

=4(2)(6)(9)=2(2)(2)(2)(3)(3)(3)

320=4(80)=4(2)(40)=2(2)(2)(4)(10)

=2(2)(2)(2)(2)(2)(5)

228=4(57)=2(3)(38)=2(2)(3)(19)

All three of them have 2*2 in commom, so the greatest common factor is 4.