Chapter 4.2, Problem 35E

To determine

To tell whether the given numbers are relatively prime or not.

Answer to Problem 35E

Yes

Explanation of Solution

Given Information: 224, 243

Formula Used: Two integers are said to be co-prime (or relatively prime) if they do not share a common divisor different than 1.

Calculation:

The factors of 224 are: $224=2\times 2\times 2\times 2\times 2\times 2\times 7$

The factors of 243 are: $243=3\times 3\times 3\times 3\times 3$

Since there is no common factor between the numbers, Then the greatest common factor is 1.

Since the two numbers have HCF 1, therefore, they are relatively prime.