Problems on Numbers Quiz Set 018

We can see that $67500 = 2^2 × 3^3 × 5^4$. The number of prime factors is sum of the powers = 9.

We can see that $1{19/x}$ = ${55/23}$ × ${8/15}$. ⇒ ${1x + 19}/x$ = ${88/69}$ ⇒ x = 69.

Let the number be N. Then it is given that 1 x N = 10. ⇒ N = 10 X 1. ⇒ ${3/8}$ x N = ${3/8}$ x 10 X 1 = ${15/4}$.

${15/4}$ is same as $3{3/4}$.

We can see that $810810000 = 2^4 × 3^4 × 5^4 × 7^1 × 11^1 × 13^1$. The number of prime factors is sum of the powers = 15.

Let the number be N. Then ${6/17}$ x N = 78. ⇒ N = 78 x ${17/6}$ = 221