What are the prime factors of 196?

1 Answer
Kaoutar Q.
Dec 1, 2016

#196=2^2xx7^2#

Explanation:

#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#

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