# Number System Practice Problems 2 | Hamaraguru

11. By what smallest number should we divide 2800 to make it as a perfect square?
a) 2
b) 4
c) 7
d) 9

12. What is smallest number, 1323 must be multiplied to make it as a  perfect cube?
a) 9
b) 3
c) 21
d) 7

13. The smallest positive integer by which 5145 must be divided to make the quotient a perfect cube is
a) 15
b) 3
c) 5
d) 7

14. What can be the maximum value of p so that 30!/2^p is an integer?
a) 25
b) 15
c) 26
d) 30

15. If x,p ∈ Ι and x>p, then find the smallest value of x such that 70!/5^p is an integer.
a) 16
b) 17
c) 18
d) 19

16. 16.    If 150!/15^x is an integral value, then find the maximum value that x can have.
a) 37
b) 10
c) 11
d) 72

17. Find the total no of zeroes after the rightmost non-zero digit in 100!.
a) 9
b) 10
c) 24
d) 25

18. If 5432*7 is divisible by 9. Find *.
a) 0
b) 1
c) 9
d) 6

19. Which one of the following is the value of * if 78*3945 is divisible by 11?
a) 1
b) 0
c) 3
d) 5

20. Which of the following is divisible by 25?
a) 303310
b) 373355
c) 303375
d) 22040