Question

Find The Maximum Power Of 501 When Divided By 500

Answer 1

Answer:

the maximum power of 501 when divided with 500! =2

Step-by-step explanation:

a)1

b)2

c)0

d)4

Answer 2

 The maximum power of 501 when divided by 500! is 247

Given: 501 is divided by 500!

To find: The maximum power of 501 when divided by 500!

Solution:

 Find the prime factor of 501 which are 3 and 167.

Then, first, divide by 3 and add together

i.e,  applying Legendre's formula for prime factor 3

[500/3] + [166/3] +[55/3] + [18/3] + [6/3] +[2/3] = 247

166 +55 + 18 + 6 + 2 + 0 = 247

Therefore 247 is the maximum power 3 prime number.

500! is divisible by 3^247which is the maximum.

Applying Legendre's formula for prime factor 167

  [500/167] + [2/167] = 2

       2 + 0 = 2

Therefore 2 is the maximum power of 167 prime number.

∴ The maximum of two powers is 247 which is our answer.