Question

What is the greatest positive power of 5 that divides 30! exactly

Answer 1

Given,

Number = 30!

To Find,

The greatest positive power of 5 that divides a given number =?

Solution,

We know that the factorial of 30 is given by,

Number = 30! = 30*29*28*27*26*25...........2*1

From numbers 1 - 30, multiples of 5 are = 5,10,15,20,25,30

Total 5's in the numbers = 1 + 1 + 1 + 1 + 2 + 1

Total 5's in the number = 7

Hence, the greatest positive power of 5 that divides 30! exactly is7.

Answer 2

Concept Introduction:-

It is the power of the numeral that indicates the multiplicative power.

Given Information:-

We have been given that a number $30!$

To Find:-

We have to find that the greatest positive power of $5$ that divides $30!$ exactly.

Solution:-

According to the problem

The given Number $= 30! = 30*29*28*27*26*25...........2*1$

From numbers $30!$, multiples of $5$ are = $5,10,15,20,25,30$

Total $5$'s in the numbers$=1+1+1+1+2+1$

Total $5$'s in the number$=7$

Final Answer:-

The greatest positive power of $5$ that divides $30!$ is $7$.