according to euclid division lemma a=bq+r where sum of all possible values of r is 120 then value of b is
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Given : According to euclid division lemma a=bq+r where sum of all possible values of r is 120
To Find : value of b
Solution:
According to euclid division lemma a=bq+r
0≤ r < b
Hence value of r
are 0 , 1 , 2 , 3 , _________ , b - 1
Hence total possible values = b
Sum = (b/2)( 0 + b - 1)
= b(b - 1)/2
b(b - 1)/2 = 120
=> b(b -1) = 240
=> b² - b - 240 = 0
=> b² - 16b + 15b - 240 = 0
=> (b - 16)(b + 15) = 0
=> b = 16 as b can not be negative
Hence Value of b is 16
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