What is the greatest power of 5 which can divide 80! exactly.

Question

What is the greatest power of 5 which can divide 80! exactly. (A) 16 (B) 20 (C) 19 (D) none of these

Tardigrade Admin · Accepted Answer

All the 16 multiplies of 5 from 1 to 80 will have a factor of 5, 25, 50 and 75 will have a second factor of 5. So the factor 5 occurs 16 + 3 = 19 times in 80! , and 19 is the greatest power of 5 that can divide 80! exactly

Q. What is the greatest power of 5 which can divide 80! exactly.

16

20

19

none of these

All the 16 multiplies of 5 from 1 to 80 will have a factor of 5, 25, 50 and 75 will have a second factor of 5. So the factor 5 occurs 16 + 3 = 19 times in 80! , and 19 is the greatest power of 5 that can divide 80! exactly