if a number is divisible by 11, is it divisible by 121
Yes, if a number is divisible by 11, it is also divisible by 121. This is because 121 is the square of 11.
Yes, if a number is divisible by 11, it is also divisible by 121.
Yes, if a number is divisible by 11, then it is also divisible by 121. This is because 121 is the square of 11.
To understand why this is true, we can look at the divisibility rule for 11. A number is divisible by 11 if the difference between the sum of its odd-positioned digits and the sum of its even-positioned digits is either 0 or a multiple of 11.
For example, let's take the number 132. The sum of the odd-positioned digits (1 and 2) is 3, and the sum of the even-positioned digit (3) is 3 as well. The difference between these sums is 0, so 132 is divisible by 11.
Now, if a number is divisible by 11, it means that the difference between the sum of its odd-positioned digits and the sum of its even-positioned digits is either 0 or a multiple of 11.
When we square a number, the odd-positioned digits and the even-positioned digits of the original number are preserved. Since the difference between the sums of these digits was either 0 or a multiple of 11 for the original number, the same will be true for its square.
Therefore, if a number is divisible by 11, its square will also be divisible by 11. In this case, if a number is divisible by 11, it will also be divisible by 121, because 121 is the square of 11.