Number of ways in which the number 831600 can | vedclass

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(D) First,find the prime factorization of $831600$: $831600 = 2^4 	imes 3^3 	imes 5^2 	imes 7^1 	imes 11^1$. For two factors to be relatively prim

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$16$

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(D) First,find the prime factorization of $831600$: $831600 = 2^4 	imes 3^3 	imes 5^2 	imes 7^1 	imes 11^1$. For two factors to be relatively prime,each prime power factor (e.g.,$2^4, 3^3, 5^2, 7^1, 11^1$) must belong entirely to one of the two factors. There are $5$ distinct prime power factors. Each of these $5$ factors can be placed in either the first factor or the second factor,giving $2^5 = 32$ ways. Since the order of the two factors does not matter (splitting into $A$ and $B$ is the same as splitting into $B$ and $A$),we divide by $2!$. Number of ways $= \frac{2^5}{2} = \frac{32}{2} = 16$.

Number of ways in which the number $831600$ can be split into two factors which are relatively prime is

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