if 2n 26 35 54 73 117 explain why 235711 is a factor of

if 2n= 2⁶ * 3⁵ * 5⁴ * 7³ * 11⁷, explain why 2*3*5*7*11 is a factor of n.

Solution

We have given,

2n= 26 * 35 * 54 * 73 * 117

=> n= 1/2 ( 26 * 35 * 54 * 73 * 117)

=> n = 1/2 (2*13 * 5*7 * 6*9* 73*13*9)

=> n = 1/2 (2*3 *5*7 *2*3*3*3*73*13*3*3)

=> n = 1/2 * (2*3*5*7*11) * 41928.5

Clearly we can say that 2*3*5*7*11 is factor of n