Find the greatest number which divides 2011 and 2623 leaving remainders 9 and 5 respectively.
To find the greatest number which divides 2011 and 2623 leaving remainder 9 and 5 respectively.
The required number when divides 2011 and 2623 leaves remainders 9 and 5 this means
2011 – 9 = 2002 and 2623 – 5 = 2618 are completely divisible by the number.
Therefore, the required number = H.C.F. of 2002 and 2618
By applying Euclid’s division lemma
2618 = 2002 x 1 + 616
2002 = 616 x 3 + 154
616 = 154 x 4+ 0.
H.C.F. of 2002 and 2618 = 154
Hence, the required number is 154