# Number System Practice Problems

1. How many factors of 720 are even?

a) 15

b) 36

c) 8

d) 24

2. Find the sum of the even factors of 300.

a) 728

b) 625

c) 744

d) 600

3. How many factors of 600 are divisible by 5 but not divisible by 25?

a) 24

b) 15

c) 12

d) 8

4. In the first 500 natural numbers, how many numbers have only three factors?

a) 4

b) 5

c) 6

d) None of these

5. If a 100 digit number consisting of all 7’s is divided by 8, what is the remainder?

a) 5

b) 1

c) 3

d) 4

6. Find the last non–zero digit in 100!

a) 3

b) 4

c) 2

d) 5

7. How many consecutive zeroes are at the end of 100!?

a) 20

b) 12

c) 22

d) 24

8. Find the unit digit of the number \(\ 17^{2003} \).

a) 7

b) 9

c) 3

d) 1

9. What is the unit digit in the expansion of \(\ 8^{2^{4^{8^{16}}}} \)

a) 8

b) 4

c) 2

d) 6

10. Find the unit digit of 1! + 2! + 3! + 4! + 5! + 6! + …..+ 100!?

a) 3

b) 9

c) 4

d) 0

11. If \(\ 17^{15} \) + \(\ 13^{15} \) is divided by 15, what is the remainder?

a) 3

b) 9

c) 0

d) 1

12. If \(\ 18^{201} \) is divided by 7, what is the remainder?

a) 0

b) 1

c) 3

d) 9

13. Ajay purchased a box of sweets and gave half the number of sweets to his wife, three sweets to his first son, one-third of the remaining to his second son and two to his third son. Find the number of sweets he purchased, if he is finally left with 4 sweets.

a) 12

b) 14

c) 16

d) 24

14. When a number is divided by 34, the remainder is 13. If thrice the same number is divided by 17, the remainder is

a) 5

b) 3

c) 7

d) 2

15. Find the least possible number which when divided by 7 and 5, leaves a remainder of 2 and 1

respectively.

a) 16

b) 9

c) 23

d) 37

16. If 100! is divisible by \(\ 12^{n} \), what is the maximum value of n?

a) 97

b) 24

c) 48

d) 12

17.If 481A769B is divisible by 5,6 and 9 then A+B is ____?

a) 0

b) 1

c) 2

d) 3

18.Find the smallest no which when divided by 3,5,7,9 and 11 leaves respective remainder of 2,4,6,8 and 10.

a). 2265

b) 2275

c) 2274

d) 3464

19.Find the largest no which when 145,121,97 are divided the remainders are same.

a) 48

b) 12

c) 36

d) 24

20. 5 bells toll at intervals of 5,6,10,15 and 20 seconds respectively. If they toll together at the same time, after how many seconds will they toll together again for the first time?.

a) 400

b) 120

c) 60

d) 30

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