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2014-10-15T23:24:40+05:30

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The equation can be facorize as 3*5*3*2*2*2*7*2*5*2*5*5*5 or 2^5*3^2*5^5*7^1 total no of prime factor =(5+1)*(5+1)*(2+1)*(1+1)=216
6 3 6
The equation can be facorize as 3*5*3*2*2*2*7*2*5*2*5*5*5 or 2^5*3^2*5^5*7^1 total no of prime factor =(5+1)*(5+1)*(2+1)*(1+1)=216
2014-10-16T11:43:50+05:30

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Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
Express the given number N as a product of prime numbers:

N
(3 * 5)12 (2 * 7)10 (10)25=3*5*2^2*3*2*7*2*5*2*5*5*5\\ \\=2^5*3^2*5^5*7\\

A prime factor of N is obtained by multiplying  (none or one or two or three or four or five of 2s ) * (none or one or two of 3s ) * (none or one or more of 5s ) * (none or one 7 )

So the number of distinct prime factors will be 

         = (1+5)(1+2)(1+5)(1+1)  = 6 * 3 * 6 * 2  
 
       = 216

7 3 7