Question

Divide the smallest number by 1, 3, 4, 5, and 6, leaving the remainder 1 in each place; But is there no partition by 11?​

Answer 1

Step-by-step explanation:

Let the number is

.<br> When

is divided by

, it leaves remainder

.<br> When

is divided by

, it leaves remainder

.<br> When

is divided by

, it leaves remainder

.<br> When

is divided by

, it leaves remainder

.<br> When

is divided by

, it leaves remainder

.<br> The remainder in each case is

.<br>

is the

of

<br>

of

<br>

, where

is a natural number.<br>

<br> Now, we have to find a value of

such that

is divisible by

.<br> For

,

, that is divisible by

.<br>

is the required number.<br>