Question

What is the greatest possible positive integer n if 16^n divides (44)^44 without leaving a remainder.

Answer 1

Answer:

29

Step-by-step explanation:

Given What is the greatest possible positive integer n if 16^n divides (44)^44 without leaving a remainder.

 Now we have

 44^44 / 8^n  

= (4 x 11)^44 / (2^3)^n

= (2^2)^44 x 11^44 / 2^3n

= 2^88 x 11^44 / 2^3n

= 2^88 – 3n x 11^44

Now 88 – 3 n >=0 and 88 – 3n<=0 will leave a remainder

So n = 88/3 = 29

 n = 29

Answer 2

Answer:  22

Step-by-step explanation:

16^n=(2^4)^n

44^44=(11*2^2)^44=11^44*2^88

(11^44 *2^88)/ 2^4n

4n=88

n=22