Answer:
The answers are 13 and 65.
Step-by-step explanation:
You can start by listing the factors of each number. The factors of fifty-four are one, two, three, six, nine, eighteen, twenty-seven, and fifty-four. Both two and fifty-four are even numbers, so they are not relatively prime. They have two as a common factor, in addition to one. The number thirteen is a prime number, and thirteen is not a factor of fifty-four. So, thirteen and fifty-four are relatively prime. Their only common factor is one. The number twenty-seven is equal to three cubed, and three is also a factor of fifty-four. So, twenty-seven and fifty-four are not relatively prime because they have common factors of both one and three. The factors of thirty-three are one, three, eleven, and thirty-three. So, thirty-three and fifty-four are not relatively prime because they also have common factors of both one and three. The factors of sixty-five are one, five, thirteen, and sixty-five. None of these factors, except one, are common to fifty-four. So, sixty-five and fifty-four are relatively prime. Finally, the number eighty-one is equal to three times twenty-seven, so eighty-one and fifty-four are not relatively prime because they, too, have common factors of both one and three. Therefore, only the numbers thirteen and sixty-five are relatively prime to fifty-four.
