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The sum of all natural numbers 'n' such that $100<n<200 \; and H.C.F (91,n)>1\; is :$
Option 1)
$3121$
Option 2)
$3203$
Option 3)
$3303$

Option 4)
$3221$

Answers (1)

S solutionqc

Natural number between 100 and 200

$=101,102,....199$

Number should either divide by 7 or divide by 13

$for \; H.C.F \; (91,n)>\; 1$

(sum of no.divisible by 7)+(sum of no divisible by 13)-(sum of no divisible by 91)

$=\sum_{r=1}^{14}(98+7r)+\sum_{r=1}^{8}(91+3r)=(182)$

$=98\times14+7\times\frac{14\times15}{2}+91\times8+13\times\frac{8\times9}{2}-182$

$=3121$

Option 1)
$3121$
Option 2)

$3203$

Option 3)

$3303$

Option 4)

$3221$

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