Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.

Question:

Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.

Solution:

We need to find the greatest number that would divide 43, 91 and 183 leaving the same remainder every time.
We first find the difference of the numbers and then find the HCF of the got numbers.

$183-91=92$

$183-43=140$

$91-43=48$

Now find HCF of 92, 140 and 48, we get

$92=2 \times 2 \times 23$

$140=2 \times 2 \times 5 \times 7$

$48=2 \times 2 \times 2 \times 2 \times 3$

HCF(92, 140, 48) = 4
Therefore, 4 is the required number. 

 

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