Question

Find the number of ways in which the number $300300$ can be split into two factors which are relatively prime

• A. $64$
• B. $32$
• C. $24$
• D. $56$

Answer 1

Answer: (B)

$32$

$300300$

$300300={\left(2\right)}^2\times 3\times 5\times 7\times 11\times 13$

Possible number used

$2⟶(2{)}^0,(2{)}^{1}3⟶(3{)}^0,(3{)}^{1}5⟶(5{)}^0,(5{)}^{1}7⟶(7{)}^0,(7{)}^{1}11⟶(11{)}^0,(11{)}^{1}13⟶(13{)}^0,(13{)}^1$

Number of divisior

$=2\times 2\times 2\times 2\times 2\times 2=64$

But in this if we write

$A\times B⟶B\times A$ is also included

which means Required divisior$=\frac{64}{2}=32$