Problem Solving QUestion assistance re

Question

Please refer: everything-about-factorials-on-the-gmat-85592.html 12=2^2*3 . We need to find maximum power of both 4 and 3 and consider the one, which is lesser. \frac{200}{2}+\frac{100}{2}+\frac{50}{2}+\frac{25}{2}+\frac{12}{2}+\frac{6}{2}+\frac{3}{2}=100+50+25+12+6+3+1=197 Thus, we have 197 as the maximum power of 2. 197/2=98 is the maximum power of 2^2 i.e. 4 Likewise, we need to find the maximum power of 3: \frac{200}{3}+\frac{66}{3}+\frac{22}{3}+\frac{7}{3}=66+22+7+2=97 97 is the maximum power of 3 for 200!. Since we need both 3 and 2^2 together for a number to be divisible by 12; we will have to consider lesser of the two maximums. Thus, maximum power of 12 is 97 that will divide 200!.

kichha51 · Answer

fluke thanks!! that was great!!!

bellcurve · Answer

First, Isn't OC 98?

Second, what is the rationale behind your 200/2+100/2.... to get the power of 2?

Thanks.

fluke · Answer

Yes, my answer doesn't match with the OA. I expected someone to point error in my solution. Truth is: I just memorized the method to calculate the maximum power of the prime number. Please check the link I earlier posted to get the details as to why we need to do so. Here it is again: everything-about-factorials-on-the-gmat-85592.html If I were to explain you, I'd say this: Max power of 2 in 10! 10/2+10/2^2+10/2^3= 5+2+1=8 Why so: 10!=10*9*8*7*6*5*4*3*2*1 2,4,6,8,10: Each has one 2. 4,8: Each has one additional 2 8: Each has one more 2.

puneetj · Answer

good explanation.

Problem Solving QUestion assistance re

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