Find the largest number that will divide 623,729 and 841 leaving remainder 3,9 and 1 respectively? Explain with process?

Dear Student,

Given numbers: 623,729 and 841

On dividing these given numbers by the largest number, we get remainder as 3,9 and 1 respectively.

From the given numbers, we now subtract their respective remainders to get the numbers which are divisible by the largest number:

623-3 = 620
729-9 = 720
And, 841-1 = 840

Now to find the largest number, we will take the H.C.F of  620,720 and 840.
$$\begin{gathered} Prime factirization of 620 = 2*2*5*31 \\ Prime factirization of 720= 2*2*2*2*3*3*5 \\ Prime factirization of 840 = 2*2*2*3*5*7 \\ Therefore, HCF = 2*2*5 = 4*5 = 20 \end{gathered}$$

Therefore, 20 is the largest number required. 

 Regards