Find the greatest number which divides 2011 and 2623 leaving remainder 9 and 5.

To do:   Find the greatest number which divides 2011 and 2623 leaving remainder 9 and 5.

Solution:

The greatest number that divides 2011 $-$ 9 = 2002 and 2623 $-$ 5 = 2618 is the HCF of 2002 and 2618

Prime factorization of 2002 and 2618 

2002 = 2 $\times$ 7 $\times$ 11 $\times$ 13 

2618 =2 $\times$ 7$\times$ 11 $\times$17

So the HCF of 2002 and 2618 is 2 $\times$ 7 $\times$ 11 or 154

The greatest number that divides 2011 And 2623 leaving remainders 9 and 5 respectively is 154.

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Updated on: 10-Oct-2022

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