Question

If all the numbers formed by rearranging the digits 4,5 and 6 are added together, then the resultant number is divisible by 111 only. State true or false.

• A. True
• B. False

Answer 1

The correct option is B False

The digits given are 4, 5 and 6.
The possible numbers are 456,465,546,564,654 and 645
Sum = 456+465+546+564+654+645
= 3330
= 111$\times$30

Now, 3330 is divisible by 111 (prime factor).
Since number 3330 is divisible 111, it will be divisible by the factors of 111, i.e., 37 and 3.
Therefore, we can say the number obtained will be divisible by 3, 37 and 111.