A six digit number abcabc such that a- b- c - N- then which is the correct statement-A- It is divisible by 6B- It is divisible by 91C- It is divisible by 143D- Only a and b are correct-

The correct option is D Only (a) and (b) are correct.abcabc = abc × 1000 + abc = abc(1000 + 1) = abc × 1001 So, any number of the form "abcabc" must be divisib ...

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Divisibility Rule for Composite Numbers

A six digit n...

Question

A six digit number abcabc such that $a, b, c ϵ N$ , then which is the correct statement?

It is divisible by 91

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It is divisible by 143

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It is divisible by 6

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Only (a) and (b) are correct.

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Solution

The correct option is D Only (a) and (b) are correct.
$a b c a b c = a b c \times 1000 + a b c$
$= a b c (1000 + 1) = a b c \times 1001$
So, any number of the form "abcabc" must be divisible by 1001 or its factors i.e. $1001 = 7 \times 13 \times 11$
So, it is divisible by 91 i.e. $(13 \times 7)$ and 143 i.e. $(13 \times 11)$

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A six digit number abcabc such that a,b,c ϵN, then which is the correct statement?

The correct option is D Only (a) and (b) are correct.abcabc=abc×1000+abc =abc(1000+1)=abc×1001 So, any number of the form "abcabc" must be divisible by 1001 or its factors i.e. 1001=7×13×11 So, it is divisible by 91 i.e. (13×7) and 143 i.e. (13×11)

A six digit number abcabc such that $a, b, c ϵ N$ , then which is the correct statement?