Question

Which is divisible by 11 :- 530664 , 53063 , 53067 , 53061

Answer 1

$\underline{ \pink{Divisibility \: by \: 11: }}$

If the difference between the sum of digits in odd places and sum of digits in even places of a number is a multiple of 11 or equal to zero ,then the given number is divisible by 11.

$1 ) Given \: number \: 530664.$

$i) Sum \: of \: the \: digits \: at \: odd \: places$

$(from \: left ) = 5+0+6 = 11$

$ii) Sum \: of \: the \: digits \: at \: even \: places$

$(from \: left ) = 3+6+4 = 13$

$iii) Difference = 13 - 11$

$= 2$

$\blue{ ( Which \: is \: not \: divisible \: by\:11 ) }$

$\red{ \therefore The \: number \: 530664 \: is \: not \: divisible \: by \: 11 }$

$2 ) Given \: number \: 53063.$

$i) Sum \: of \: the \: digits \: at \: odd \: places$

$(from \: left ) = 5+0+3 = 8$

$ii) Sum \: of \: the \: digits \: at \: even \: places$

$(from \: left ) = 3+6 = 9$

$iii) Difference = 9-8$

$= 1$

$\blue{ ( Which \: is \: not \: divisible \: by\:11 ) }$

$\red{ \therefore The \: number \: 53063 \: is \: not \: divisible \: by \: 11 }$

$3) Given \: number \: 53067.$

$i) Sum \: of \: the \: digits \: at \: odd \: places$

$(from \: left ) = 5+0+7 = 12$

$ii) Sum \: of \: the \: digits \: at \: even \: places$

$(from \: left ) = 3+6= 9$

$iii) Difference = 12 - 9$

$= 3$

$\blue{ ( Which \: is \: not \: divisible \: by\:11 ) }$

$\red{ \therefore The \: number \: 53067 \: is \: not \: divisible \: by \: 11 }$

$4 ) Given \: number \: 53061$

$i) Sum \: of \: the \: digits \: at \: odd \: places$

$(from \: left ) = 5+0+1 = 6$

$ii) Sum \: of \: the \: digits \: at \: even \: places$

$(from \: left ) = 3+6= 9$

$iii) Difference = 9-6$

$= 3$

$\blue{ ( Which \: is \: not \: divisible \: by\:11 ) }$

$\red{ \therefore The \: number \: 53061\: is \: not \: divisible \: by \: 11 }$

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