Question

What is the greatest positive integer less than 100 that has an odd number of positive divisors. explain step by step .​

Answer 1

Answer:

81

Step-by-step explanation:

If number is perfect square it has odd number of divisiors .

So greatest perfect square less then 100 is 81 .

Check

Start by 99

divisors 1 , 3 , 9 , 33 ,11 , 99

So it's not our answer .

98 = 1 , 2 ,7 , 14 , 49 , 98

97 = 1 , 97

96 = 1 , 2 , 3 , 6 , 8 , 12 , 24 , 32 , 48 , 96

95 = 1 , 5 , 19 , 95

94 = 1 , 2 , 47 , 94

93 = 1 , 93

92 = 1 , 2 , 2 , 23 , 46 , 92

91 = 1 , 91

90 = 1 , 2 , 3 , 5,6 , 10 , 18 , 30 , 45 , 90

89 = 1 , 89

88 = 1 , 2 , 4 , 8, 11 , 22 ,44 , 88

87 = 1 , 3 , 29 , 87

86 = 1 , 2 , 43 , 86

85 = 1 , 5 , 17 , 85

84 = 1 , 2 , 3, 4, 6 , 7 , 12,14 , 21,28 , 42 ,84

83 = 1 , 83

82 = 1 , 2 ,41 ,82

81 = 1 , 3 , 9, 27,81

There are such √100 = 10 numbers .

Answer 2

Answer: 81
81/3=27
I hope this will be helpful for you