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/Medical Exams

Maths

Solution

123

4.0 (1 ratings)

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 .