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Find the largest number which divides 320 and 457 , leaving remainders 5 and 7 respectively.

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Find the largest number which divides 320 and 457 , leaving remainders 5 and 7 respectively.
in Mathematics by Platinum (102k points) | 354 views

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The largest number which divides 320 and 457 leaving remainders5 and 7 respectively \(=\mathrm{HCF}\) of \((320-5)\) and \((457-7)\) \(=\mathrm{HCF}\) of 315 and 450 \(450=315 \times 1+135\) \(315=135 \times 2+45\) \(135=45 \times 3+0\)
\(\therefore\) HCF of 450 and 315 is 45 .
So, the largest number which divides 320 and 457 leaving remainders 5 and 7 respectively is 45 .
by Platinum (102k points)

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