Q. 154.0( 5 Votes )

Find the greatest

Answer :

It is mentioned in the question that that on dividing 2053 by the required number there is a remainder of 5 which means that 2053 - 5 = 2048 is exactly divisible by required number . In the similar manner,


967 - 7 = 960 the required number is the largest number satisfying the above property.


Therefore, it is the HCF of 2048 & 960


2048 = 64 × 32


= 26 × 25


= 211


960 = 5 × 2 × 2 × 2 × 2 × 2 × 2 × 3


So for finding the HCF we may write as follows:


Common Factor Least Power


2 6


So HCF = 26


= 64


HCF of 2048 & 960 is 64


Hence required number is 64


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