Question 53043: Two positive integers M and N are defined to be relatively prime if GCF(M, N) = 1. Which two pairs are numbers below are relatively prime?
a. 17 and 51
b. 6 and 25
c. 18 and 45
d. None of the above. In order for two numbers to be relatively prime, at least one of them has to be prime
Found 3 solutions by consc198, math_iz_hard, ikleyn:
Answer by consc198(59)   (Show Source):
Answer by math_iz_hard(8) (Show Source):
Answer by ikleyn(53937)  (Show Source):
You can put this solution on YOUR website! .
Divisibility_and_Prime_Numbers/53043: Two positive integers M and N are defined to be relatively prime
if GCF(M, N) = 1. Which two pairs are numbers below are relatively prime?
a. 17 and 51
b. 6 and 25
c. 18 and 45
d. None of the above. In order for two numbers to be relatively prime, at least one of them has to be prime
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The answer in the post by @consc198 is FATALLY WRONG.
The pair (17,51) has GCF (Greatest Common Factor) of 17, so these numbers are NOT relatively prime.
The pair (6,25) has GCF (Greatest Common Factor) of 1, so these numbers are relatively prime.
The pair (18,45) has GCF (Greatest Common Factor) of 9, so these numbers are NOT relatively prime.
Thus of the three given pairs of numbers, only one pair has relatively prime companions.
This pair is option (b)
Notice that the question is posed/worded incorrectly in the problem:
it asks "which two pairs below are relatively prime?",
while there is ONLY ONE such pair among the listed.
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