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.

Solution

Clearly, the required number is the H.C.F of the numbers
2007=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:
425= 391 1+34
391 = 3411 +17
34 =172+0
Clearly, H.C.F of391 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*31 +0
The H.C.F of 17 and 527 is 17. Hence, H.C.F of 391,425 and 527 is 17.
Hence, the required number is 17.