# 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

Answer Key:

11.c

12.d

13.a

14.c

15.b

16.a

17.c

18.d

19.d

20.c

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