To derive the divisible characteristics of a number, it is necessary to observe the relationship between the number and 1 1.
First of all, we know that the multiple of 1 1 is characterized in that the difference between the single digit and the ten digit of a number is a multiple of 1 1. That is, if the result of subtracting ten digits from one digit of a number is a multiple of 1 1, then the number is a multiple of 1 1.
For example:
22, the unit number is 2, the decimal number is also 2, 2-2=0, and 0 is a multiple of 1 1, so 22 is a multiple of 1 1.
33, the unit number is 3, and the decimal is 3, 3-3=0, and 0 is a multiple of 1 1, so 33 is a multiple of 1 1.
44, the unit number is 4, and the decimal number is 4, 4-4=0, and 0 is a multiple of 1 1, so 44 is a multiple of 1 1.
According to this feature, we can draw a conclusion that if the result of subtracting ten digits from one digit of a number is a multiple of 1 1, then the number is 1 1.
The unit number is 5, the decimal number is 4, and the result of subtracting the decimal number from the unit number is 5-4= 1, not a multiple of 1 1, so 12345 is not a multiple of 1 1.
To sum up, if the result of subtracting ten digits from one digit of a number is a multiple of 1 1, then this number is a multiple of 1 1.
Extended data:
For a large number, some carefully processed eigenvalues (actually constructed by using the bit value principle) can really reveal its divisibility.
We call the last bit (S), bit (segment) and bit (segment) (parity) difference of a large number as the eigenvalue of this large number. If the eigenvalue can be divisible by some numbers, then this large number can also be divisible. If the remainder of the eigenvalue divisible by B is R, then the remainder of this large number divisible by B is also R (or B-r).
So the eigenvalues are like facial features of a large number. I don't need to look at the whole body of a large number, just look at the face to know its divisibility and remainder characteristics.
Briefly mention the proof and construction skills. We decompose a large number A into the sum or difference of two parts, and it is known that most of them are multiples of a given divisor B, so we only need to judge that the remaining small part (this part is called eigenvalue) is also a multiple of B, and then extract the common factor to judge B | A. ..