Question

The largest number which divides 318 and 739 leaving remainders 3 and 4 respectively is?

Can anyone gimme a satisfactory step by step Answer?

Juniors plj- dun put ur blôôdy @&& inside if uh dun know-
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Answer 1

105 is the largest number which divides 318 and 739 leaving remainder 3 and 4 respectively.

Step-by-step explanation:

To find : The largest number which divides 318 and 739 leaving remainder 3 and 4 respectively ?

Solution :

Number which divides 318 and 739 leaving remainder 3 and 4 respectively

318-3=315

739-4=735

Now, We find the Highest common factor of the numbers 315 and 735

315=3×3×5×7315=3\times 3\times 5\times 7315=3×3×5×7

735=3×5×7×7735=3\times 5\times 7\times 7735=3×5×7×7

HCF(315,735)=3×5×7HCF(315,735)=3\times 5\times 7HCF(315,735)=3×5×7

HCF(315,735)=105HCF(315,735)=105HCF(315,735)=105

Therefore, 105 is the largest number which divides 318 and 739 leaving remainder 3 and 4 respectively.

Answer 2

$\textsf{Given that, if 318 divided by something gives remainder 3 and also the same with }\\\textsf{the number 739 gives remainder 4 then subtracting the remainder from the respective}\\\textsf{number makes it a prefect dividend of the required number.}\\\textsf{i.e.}$

    $\textsf{\texttt{739 - 4} and \texttt{318 - 3}}\\\textsf{Evaluates to, 735 and 315 }\\\textsf{And Prime factorizing the results gives,}\\\texttt{\: \: 735 - 7 \cdot 3 \cdot 5 \cdot 7}\\\texttt{\: \: 315 - 3 \cdot 3 \cdot 5 \cdot 7}\\\textsf{Then HCF of 315 and 735 is the required number\texttt{ = 3 \cdot 5 \cdot 7 = 105}}$

 $\textsf{Hence the required number is \texttt{105}.}$