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Find the greatest number which divides 2011 and 2623 leaving remainders 9 and 5 respectively.
Given: 2011 and 2623.
To find: Here we have to find the value of the greatest number which divides 2011 and 2623 leaving remainders 9 and 5 respectively.
Solution:
If the required number divide 2011 and 2623 leaving remainders 9 and 5 respectively, then this means that number will divide 2002(2011 $-$ 9) and 2618(2623 $-$ 5) completely.
Now, we just have to find the HCF of 2002 and 2618.
Finding HCF of 2002 and 2618 using Euclid's division lemma:
Using Euclid’s lemma to get:
- $2618\ =\ 2002\ \times\ 1\ +\ 616$
Now, consider the divisor 2002 and the remainder 616, and apply the division lemma to get:
- $2002\ =\ 616\ \times\ 3\ +\ 154$
Now, consider the divisor 616 and the remainder 154, and apply the division lemma to get:
- $616\ =\ 154\ \times\ 4\ +\ 0$
The remainder has become zero, and we cannot proceed any further.
Therefore the HCF of 2002 and 2618 is the divisor at this stage, i.e., 154.
So, the greatest number which divides 2011 and 2623 leaving remainders 9 and 5 respectively is 154.
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