1.

Find the largest number that divide 445 ,572 and 699 leaving remainders 4,5 and 6 respectively

Answer»

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Given that :- On dividing 445 by the required number, than there is a remainder of 4.

This means that 445 - 4 = 441, is EXACTLY DIVISIBLE by the required number.

Similarly like this only :-

572 - 5 = 567

699 - 6 = 693

REQUIRED NUMBER ⇒ LARGEST NUMBER.

H.C.F of 441,567, and 693. are :-

441 = 3 x 3 x 7 x 7  

572 = 3 x 3 x 3 x 3 x 7  

693 = 3 x 3 x 7 x 11  

Common Factors are 3 x 3 x 7 = 63

∴ H.C.F = 63.

Hence, 63 is the largest number that DIVIDE 445 ,572 and 699 leaving remainders 4,5 and 6 respectively.


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