Question

Helle, d y J 3 W ICU spuis on all the three wheels touch the ground. Find the largest number that will divide 398, 436 and 542 leaving remainders 7,11 and 15 respectively.

NEET

Maths

Solution

154

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Clearly, the required number is the H.C.F of the numbers ( 398-7=391,436-11=425 . ) and ( 542-15=527 ) First we find the H.C.F. of 391 and 425 by Euclid's algorithm as given below: [ begin{array}{l} 425=391 times 1+34 391=34 times 11+17 34=17 times 2+0 end{array} ] Clearly, H.C.F of 391 and 425 is 17 . Let us now find the H.C.F of 17 and the third number 527 by Euclid's algorithm: [ 527=17 times 31+0 ] The H.C.F of 17 and 527 is ( 17 . ) Hence, ( mathrm{H.C.F} ) of 391,425 and 527 is ( 17 . ) Hence, the required number is 17 .