find the highest power of 5 that divides each of the followi

find the highest power of 5 that divides each of the following integers:31575, 31465, 128125

Solution

31575/5=6315

6315/5=1263

1263/5=252.6

252.6/5=50.52

50.52/5=10.104

10.104/5=2.0208

# of Factors of 5 in 31575! = int (31575) 5 + int (31575)/ 25 + int (31575)/ 125 + int (31575)/625 +int(31575)/5^6

31575/5+31575/5^2+31575/5^3+31575/5^4+31575/5^5+31575/5^6

=6315+1263+252+50+10+2

=7892

Therefore, the largest power of 5 that divides 31575 is 5^7892

solution2:

the largest power of 5 that divides 31465 is

31465/5=6293

the largest power of 5 that divides 31465 is 5^7864

Solution3

the largest power of 5 that divides 128125 is 5^32029