Question

Fing the least number that should be added to 65980 so that the sum is exactly divisible by 258.
OPTIONS:
*66
*68
*70
*68

Answer 1

$Given \: number \: 65980$

$\underline {\blue { We \:find \: by \:division\: method :}}$

2 | 65980 | 257

×2| 4

________

45| 259

×5| 225

________

507 | 3480

×7 | 3549

__________

******** (-69)

$The \: Remainder \: is \: (-69)$

$This \:means \: , if \: we \:add \: \green {69} \: to \\65980. We \: get \: perfect \:square .$

$Now, \green { Perfect \:square \: (65980 + 69) } \\= 66049 \\= (257)^{2}$

Therefore.,

$Hence, the \: required \\least \: number \: is \: 69$

$\red{Note : } Given \: options \: are \:wrong .$

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