Question

find the highest power of 72 in 200 factorial​

Answer 1

Answer:

ok

Step-by-step explanation:

the highest power of 72 in 200 factories is 2

Answer 2

To Find:

The highest power of 72 in 200 factorial​

Factorial notation

The notation n! represents the product of first n natural numbers, i.e., the product 1 × 2 × 3 × . . . × (n – 1) × n is denoted as n!. We read this symbol as ‘n factorial’.

Thus, 1 × 2 × 3 × 4 . . . × (n – 1) × n = n !

For example,

1! = 1

2! = 1 x 2 = 2

3! = 1 x 2 x 3 = 6

4! = 1 x 2 x 3 x 4 = 24, which are the factors of the given number.

Solution:

200!

n! =[ $\frac{n}{k}$] + [$\frac{n}{k^{2} }$] +.....∞

we write up to the power 2, Because 72² = 5184 which is greater than value of n.

      =[ $\frac{200}{72}$]

      = 2.777

we take, only the value before the point

so,  the highest power of 72 in 200 factorial​ is 2