How can the GCF be used to write a fraction?
Divide both the numerator and denominator by their GCF to get a fraction in lowest terms.
The GCF (greatest common factor) can be used to express a fraction in simplest terms:
Find the GCF of the numerator and denominator.
Divide both the numerator and denominator by the GCF.
For example, to express
My favourite method to find the GCF of two numbers goes as follows:
Divide the larger number by the smaller to get a quotient and remainder.
If the remainder is zero, then the smaller number is the GCF.
Otherwise, repeat with the smaller number and the remainder.
So in my example:
#70/42 = 1#with remainder #28#
#42/28 = 1#with remainder #14#
#28/14 = 2#with remainder #0#
So the GCF of
Having found the GCF, we can now write:
#70/42 = ((70/14)) / ((42/14))= 5/3#
Alternatively, we can express the division implicitly:
#70/42 = (5 xx color(red)(cancel(color(black)(14))))/(3 xx color(red)(cancel(color(black)(14)))) = 5/3#