Concept explainers
Tojustify:the given statement.
Explanation of Solution
Given information:
The given statement:
“If each of two integers is divided by their GCF, the two quotients are relatively prime.”
Concept used:
Two integers are relatively prime if their greatest common factor is 1
Proof:
By definition, the greatest common factor (GCF) of two integers is the greatest integers that is a factor of each.
If we divide each of the two integers by their GCF, the quotient of each is a number that is not common to both the integers.
If now, the GCF of the quotients is taken, as they have no common factors, the GCF will be 1
Therefore, the quotients are relatively prime.
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