find all three digit numbers less than 200 that can be expressed as a²b, where a and b are prime numbers.
Answers
Given : Three digit numbers less than 200 that can be expressed as a²b, where a and b are prime numbers.
To Find : all three digit numbers less than 200
Solution:
Prime numbers 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 , 41 , 43 , 47
all three digit numbers less than 200
100 to 199
a²b taking a = 2
=> a² = 4 b = 29 , 31 , 37 , 41 , 43 , 47
116 , 124 , 148 , 164 , 172 , 188
a = 3
=> a² = 9 b = 13 , 17 , 19
117 , 153 , 171
a = 5
=> a² = 25 b = 5 , 7
125 , 175 ( if a and b are distinct numbers then b ≠ 5 )
a = 7
a² = 49 b = 3
147
a = 11 => a² = 121 no value of b
Total 12 numbers
116 , 124 , 148 , 164 , 172 , 188 , 117 , 153 , 171 , 125 , 175 , 147
if a and b are distinct numbers
Then 11 numbers as 125 will be excluded.
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