#color(green)2# is the SMALLEST prime number that can divide 196 so we'll start with that :
#196/color(blue)2=98#
98 also can be divided by #color(green)2#, so :
#98/color(blue)2 = 49#
#color(green)2# is no longer a divisor of 49, so we must find the next SMALLEST prime number that can divide 49, which is #color(red)7#
#49/color(blue)7=7#
Again, #color(red)7# is a divisor of itself so :
#7/color(blue)7=1#
We end the division when we find 1, and the prime factorization of the number 196 is the product of the prime factors in the denominators which are in this case #color(green)2# and #color(red)7# :
#196=color(blue)(2xx2xx7xx7)=color(blue)2^2xxcolor(blue)7^2#