# Playing With Numbers

32. If a number divides three numbers exactly, it must be divisible by

• (A) 9
• (B) 6
• (C) 3
• (D) 12

31. The sum of the factors of 6 is

• (A) 45
• (B) 60
• (C) 75
• (D) 90

30. The number of factors of 36 is

• (A) 6
• (B) 7
• (C) 8
• (D) 9

29. What is the sum of all the factors of 36?

• (A) 97
• (B) 91
• (C) 90
• (D) 89

28. Number of factors of the number 68 is

• (A) 8
• (B) 18
• (C) 28
• (D) 48

27. Which among the following is an example of a perfect number?

• (A) 8
• (B) 18
• (C) 28
• (D) 48

26. The sum of first three common multiples of 3, 4 and 9 is

• (A) 108
• (B) 144
• (C) 252
• (D) 216

25. The number of distinct prime factors of the largest 4-digit number is

• (A) 2
• (B) 3
• (C) 5
• (D) 11

24. The number of distinct prime factors of the smallest 5-digit number is

• (A) 2
• (B) 4
• (C) 6
• (D) 8

23. If the number 7254*98 is divisible by 22, the digit at * is

• (A) 1
• (B) 2
• (C) 6
• (D) 0

22. The largest number which always divides the sum of any pair of consecutive odd numbers is

• (A) 2
• (B) 4
• (C) 6
• (D) 8

21. Which of the following number is divisible by 3?

• (A) 121
• (B) 123
• (C) 124
• (D) 122

20. A number is divisible by 4 if its

• (A) last digit is 4
• (B) last digit is 0
• (C) last two digits are divisible by 4
• (D) last digit is 8

19. A number is divisible by 5 and 6. It may not be divisible by

• (A) 10
• (B) 15
• (C) 30
• (D) 60

18. The sum of the prime factors of 1729 is

• (A) 13
• (B) 19
• (C) 32
• (D) 39

17. The greatest number which always divides the product of the predecessor and successor of an odd natural number other than 1, is

• (A) 6
• (B) 4
• (C) 16
• (D) 8