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Mathematical significance of divisibility
Characteristics of numbers divisible by 1 1: If the difference between the sum of odd digits and the sum of even digits of an integer can be divisible by 1 1, then this number can be divisible by1. 1 1 can also be processed by the "tail-cutting method" in the above inspection 7! The only difference in the process is that the multiple is 1 instead of 2!

For example, whether 49 1678 is divisible by 1 1 is judged.

-→ sum of odd numbers 9+6+8=23?

-→ sum of even numbers 4+1+7 =1223-12 =11?

So 49 1678 can be divisible by 1 1. This method is called "parity difference method".

In addition to the above methods, it can also be judged by tangent subtraction. That is, subtract 65438 times, 20 times and 30 times of 10 from a number until the remainder is within 100. If the remainder can be divisible by 1 1, then the original number must be 10.

Another example is to judge whether 583 is divisible by 1 1.

1 1 minus 583 times 50(583- 1 1×50 = 33), and the remainder is 33. 33 is divisible by 1 1, and of course 583 can also be divisible by 1 1.

Extended data:

If the integer B is divisible by the non-zero integer A, the quotient is an integer and the remainder is zero, we say that B is divisible by A (or A is divisible by B), B is a dividend and A is a divisor, that is, A | B (| "is an divisible symbol), which is read as" A is divisible by B "or" B is divisible by A ". A is called the divisor (or factor) of B, and B is called the multiple of A. Divisibility is a special case of division.

Separability and separability are different and related. Division means that the quotient obtained by dividing the exponent A by the number b(b≠0) is an integer or a finite decimal, and the remainder is zero, so we say that A can be divided by B (or that B can divide A).

Therefore, the difference between divisibility and division is that divisibility is only when the dividend, divisor and quotient are integers and the remainder is zero. Division is not limited to the range of integers. Divider, divisor and quotient can be integers or finite decimals, as long as the remainder is zero. The relationship between them is a special case of divisibility.

References:

Baidu encyclopedia-divisible