largest number that will divide 603,729,841 leaving remainder 3,9 and 1respectively
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Numbers are 623,729 and 841 and remainders are 3,9,1 respectively
∴ Numbers will be 623−3=620
729−9=720
841−1=840
Now let us find the H.C.F of 620,720 and 840
The H.C.F of 620,720 and 840 is 20
∴ The required largest number =20
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Explanation:
Because the number has to be smaller than 30 we check the primes below 6 to find one that leaves a remainder of 3 for both numbers. 5 fits the bill. 33=6×5+3, 168=33×5+3 and since 6 and 33 have an LCF of 3 the largest number that divides both 33 and 168 leaving a remainder of 3 is 3×5=15.
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