Question

Find the maximum value of n such that 157! Is divisible by 12n. A) 77 b) 76 c) 75 d) 80 answer :c

Answer 1

Answer:

157/3 = 52

52/3 = 17

17/3 = 5

5/3 = 1

So,52+17+5+1 = 75

hope this helped

Step-by-step explanation:

Answer 2

Answer:

75

Step-by-step explanation:

12 = 2 x 2 x 3

Lets find out the power of “3” in 157!

157/3 = 52

52/3 = 17

17/3 = 5

5/3 = 1

So,52+17+5+1 = 75

We know that using the same method if we calculate the value for power of “2” then it would be much greater than 75.

So, we can conclude that we need n = 75 to have prefect divisible

Q2:

18 = 3 x 3 x 2

Lets find out the power of “3” in 157!

157/3 = 52

52/3 = 17

17/3 = 5

5/3 = 1

So,52+17+5+1 = 75

We know that using the same method if we calculate the value for power of “2” then it would be much greater than 75.

Now, we know that 3^75 would be in numerator. So, we would need n=37