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Question 151174This question is from textbook
: How many positive divisors does 3^6 * 12^4 * 15^2 * 27^3 * 64^5 * 25^10 have?
This question is from textbook
Answer by vleith(2983)   (Show Source):
You can put this solution on YOUR website! You need to find the number of prime factors in the full product.
3*3*3*3*3*3*1
12*12*12*12 = 2*2*3 * 2*2*3 * 2*2*3 * 2*2*3 *1
15*15 = 5*3 * 5*3 *1
27*27*27 = 3*3*3 * 3*3*3 * 3*3*3 *1
and so on 64 is 2^6 raised to the power of 5 says 2^30 *1
25^10 = (5^2)^10 5^10* 2^10 * 1
Now combine all the factors of the same base
adding the 3's we get 6+4+2+9 = 21
adding 2's we get 8+30 + 10 = 48
adding 5's we get 2+10 = 12
and we always have 1 as a factor
So the number of different products we can make with the factors at hand are:
1+21+48+12 = 82
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