Question

Consider the number N$=2910600$. Total number of ways, in which the given number can be split into two factors such that their highest common factor is a prime number is equal to.

• A. $16$
• B. $32$
• C. $48$
• D. $64$

Answer 1

The correct option is A $16$

Given number

$N=2910600$

Factor of N $N=2^3{.3}^3{.5}^2{.7}^2.11$

Here Spliting into two factors So no of ways for

$2=2^0,2^1$

$3=3^0,3^1$

$5=5^0,5^1$

$7=7^0,7^1$

$11={11}^0,{11}^1$

Hence possible no of ways$=2\times 2\times 2\times 2\times 2=32$

But in these it can be possible that number is same

So for different no

$ways=\frac{32}{2}=16$