Answer to Question #8747 in Abstract Algebra for navvya vishal

Question

Show that 343 and& 432 are co-prime.

Answer 1

We should prove that
GCD(343, 432) = 1,
i.e. that these numbers has no
prime common divisors.

Let us compute their prime
decompositions:

343 | 7
49 | 7
7 | 7
1

432 |
2
216 | 2
108 | 2
54 | 2
27 | 3
9 | 3
3 | 3
1


Thus
343 = 7^3
432 = 2^4 * 3^3

Since 343 and 432 has
no common prime divisors, and so they are coprime.