The number 111..............1 (91 times) is a - Vidyadip

MCQ

The number $111..............1$ ($91$ times) is a

A
Even number
B
Prime number
✓
Not prime
D
None of these

✓

Answer

Correct option: C.

Not prime

c
(c) $S = 1 + 10 + {10^2} + ...... + {10^{90}}$ ($91$ terms)

$ = \frac{{1.({{10}^{91}} - 1)}}{{10 - 1}} = \frac{{{{({{10}^{13}})}^7} - 1}}{{{{10}^{13}} - 1}} \times \frac{{{{10}^{13}} - 1}}{{10 - 1}}$

$ = [{({10^{13}})^6} + {({10^{13}})^5} + {({10^{13}})^4} + ......1]$

$({10^{12}} + {10^{11}} + ...... + 1)$

It is the product of two integers and hence not prime.

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