# Answer to Question #8747 in Abstract Algebra for navvya vishal

Question #8747

Show that 343 and& 432 are co-prime.

Expert's answer

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.

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.

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