Question

what is the highest power of 4 in 50!​

Answer 1

Answer:

The power of 4 in 50 in 4^2 = 16

Answer 2

Answer:

Highest power of 4 in 50! is 47.

Step-by-step explanation:

Power of a number is the number of times we multiply the number to itself.

$4^1=4\\4^2=4*4=16\\4^3=4*4*4=64$

and so on...

We can find highest power of 4 in 50! , using the following steps:

expressing 4 in terms of prime factors, i.e 2x2

Since we have both the prime numbers as 2, highest power is 2, and thus highest power of 4 in 50! will bw equal to highest power of 2 in 50!

We can find this by the formula below:

$[\frac{n}{p} ]+[\frac{n}{p^2} ]+[\frac{n}{p^3} ]+.....$

where p is the prime number

We have, n=50 and p=2

Putting the values,

$[\frac{50}{2} ]+[\frac{50}{2^2} ]+[\frac{50}{2^3} ]+[\frac{50}{2^4} ]+[\frac{50}{2^5} ]+[\frac{50}{2^6} ]+.....$

$=[\frac{50}{2} ]+[\frac{50}{4} ]+[\frac{50}{8} ]+[\frac{50}{16} ]+[\frac{50}{32} ]+[\frac{50}{64} ]$

$=25+12+6+3+1+0$

$=47$