Question

Prove that 11111111.......... 65 times is a composite number

Answer 1

look
break 11111...... in pairs of 5 or 13 whichever you like
now 11111,11111,11111,11111, upto 13 such pairs.
now 11111 is divisible by 11111 itself
so all 13 pairs or 65 times 11111 will be divisible by
1, the no. itself and 11111 so its not prime but a composite no.
now 11111... upto 13 times,will have the same no. as its fa tor apart from 1
so 11111. upto 65 times will also have 1111....13 times as its factor
also if you want more clarity then factors of 11111 are
41 and 279 also so they will also divide the no. in question