Question

Find the greatest value of x. if 61! is divisible by 10 power x​

Answer 1

Answer:

I think answer of greatest value of x is 6.1

I am not sure

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Answer 2

Given: 61! is divisible by 10 power x​

To find: The greatest value of x.

Solution: The greatest value of x is 14.

In order to solve the question, first, the number 10 must be split into its prime factors.

$10 = 2 * 5$

Since the greatest value of x must be calculated, further calculations are done with 5 (greater number). Now, 61 is divided by 5 and the floor value of the quotient is taken into consideration. The floor value is the closest integer less than or equal to a given number.

$\frac{61}{5} = 12$

Now, the quotient is again divided by 5. This is done till the quotient becomes 0.

$\frac{12}{5} = 2$

$\frac{2}{5} = 0$

Then, all the floor values are added to find the greatest value of x.

$12 + 2= 14$

Therefore, the greatest value of x is 14.