How can you simplify the following fraction using prime factorization?: #456/939#
1 Answer
Explanation:
We can factor
We can factor
It might take us a while to find that
So the only common factor is
#456/939 = (color(red)(cancel(color(black)(3)))xx152)/(color(red)(cancel(color(black)(3)))xx313) = 152/313#
Alternative method
Rather than doing all of this factoring, we can find the GCF of
-
Divide the larger number by the smaller to give a quotient and remainder.
-
If the remainder is
#0# then the smaller number is the GCF. -
Otherwise repeat with the smaller number and the remainder.
So in our example:
#939/456 = 2# with remainder#27#
#456/27 = 16# with remainder#24#
#27/24 = 1# with remainder#3#
#24/3 = 8# with remainder#0#
So the GCF is
#456/939 = ((456/3))/((939/3)) = 152/313#