Question

find the largest number which divides 320 and 457 leaving remainder 5 and 7 respectively rs aggarwal class 10
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Answer 1

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The largest number which divides 320 and 457 leaving remainder 5 and 7 respectively is

= LCM OF (320-5) & (457-7)

= LCM OF 315 & 450

Now

$315 = 3 \times 3 \times 5 \times 7$

$450 =2 \times 3 \times 3 \times 5 \times 5$

$lcm \: = 3 \times 3 \times 5 = 45$

Hence The largest number which divides 320 and 457 leaving remainder 5 and 7 respectively is 45

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